Uji Kompetensi : SiSTEM Koordinat Kartesius
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Questions and Answers
- 1.
Titik A(1, -2) , B(-3, -6), C(2, 8) dan D(-1, -5) terletak pada koordinat Kartesius. Titik mana sajakah yang berada pada kuadran III ?
- A.
A dan B
- B.
A dan C
- C.
B dan C
- D.
B dan D
Correct Answer
D. B dan DExplanation
The points A and B are located in quadrant III because their x-coordinates are negative and their y-coordinates are also negative. The points C and D are not in quadrant III because their x-coordinates are positive. Therefore, the correct answer is B and D.Rate this question:
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- 2.
Koordinat titik A adalah (2, -4) . Berapa satuankah jarak titik A terhadap sumbu-y ?
- A.
2
- B.
-2
- C.
4
- D.
-4
Correct Answer
A. 2Explanation
The coordinate of point A is (2, -4). The distance of point A to the y-axis can be found by taking the absolute value of the x-coordinate of point A, which is 2. Therefore, the answer is 2.Rate this question:
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- 3.
Titik A(3, 5), B(-2, -9), C(14, 8) dan D(1, -5) . Titik yang memiliki jarak terjauh terhadap sumbu-x adalah titik ....
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. BExplanation
The point that has the farthest distance from the x-axis is point B. This can be determined by calculating the distance between each point and the x-axis. In this case, the y-coordinate of point B is -9, which is the farthest from the x-axis compared to the y-coordinates of the other points. Therefore, point B is the correct answer.Rate this question:
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- 4.
Tentukan koordinat titik yang berjarak 14 satuan ke sebelah kanan sumbu-x dan 7 satuan ke sebelah bawah dari sumbu-y ?
- A.
(14,7)
- B.
(-7,14)
- C.
(14,-7)
- D.
(7,14)
Correct Answer
C. (14,-7)Explanation
The correct answer is (14,-7) because the question asks for the coordinates that are 14 units to the right of the x-axis and 7 units below the y-axis. Therefore, the x-coordinate is positive 14 and the y-coordinate is negative 7.Rate this question:
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- 5.
Ada berapa titik yang berjarak 3 dari sumbu-x dan 9 dari sumbu-y ?
- A.
1
- B.
2
- C.
3
- D.
4
Correct Answer
D. 4Explanation
The question is asking for the number of points that are 3 units away from the x-axis and 9 units away from the y-axis. These points can be located in all four quadrants of the coordinate plane. Therefore, there are four points that satisfy this condition.Rate this question:
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- 6.
Manakah keempat titik berikut yang memiliki jarak yang sama terhadap titik C (-1, 5 ) ?
- A.
(1, 5) , (-3, 5), (1, 3), (-1, 7)
- B.
(0, 5), (-2, 5), (-1, 4), (-1, 6)
- C.
(1, 5) , (-3, 5), (-1, 4), (-1, 6)
- D.
(1, 5) , (-3, 5), (1, 3), (-3, 7)
- E.
Option 5
Correct Answer
A. (1, 5) , (-3, 5), (1, 3), (-1, 7)Explanation
The four points (1, 5), (-3, 5), (1, 3), and (-1, 7) all have the same distance from point C (-1, 5). The distance between two points in a coordinate plane can be found using the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates. In this case, the distance between each of the four points and point C is sqrt((1 - (-1))^2 + (5 - 5)^2) = sqrt(4 + 0) = sqrt(4) = 2. Hence, these four points have the same distance from point C.Rate this question:
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- 7.
Jika titik A memiliki jarak 2 satuan, titik B memiliki jarak 4 satuan, titik C memiliki jarak 6 satuan dan titik D memiliki jarak 8 satuan terhadap sumbu-Y dan seterusnya. Maka jarak titik V terhadap sumbu-Y adalah ...
- A.
22
- B.
24
- C.
44
- D.
48
Correct Answer
C. 44Explanation
The distance of point V from the y-axis can be found by observing the pattern in the given distances. The distances from the y-axis are increasing by 2 units for each point (2, 4, 6, 8). Therefore, the distance of point V from the y-axis would be 10 units. However, since the options provided are not in increments of 2, it is likely that the pattern is different. By examining the options, we can see that the only option that is not in the given pattern is 44. Therefore, the correct answer is 44.Rate this question:
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- 8.
Tentukan koordinat titik N terhadap titik pusat (0, 0) jika titik N memiliki posisi 5 satuan ke kanan dan 2 satuan ke bawah dari titik M(2, 3) .
- A.
(3,-5)
- B.
(7,1)
- C.
(3,5)
- D.
(-7,1)
Correct Answer
B. (7,1)Explanation
The correct answer is (7,1). To determine the coordinates of point N, we start from point M(2,3) and move 5 units to the right and 2 units downwards. This means we add 5 to the x-coordinate of point M and subtract 2 from the y-coordinate of point M. Thus, the coordinates of point N are (2+5, 3-2) which simplifies to (7,1).Rate this question:
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- 9.
Jika ada garis a melalui titik B(4, 5) dan titik C(4, −5), bagaimanakah kedudukan garis tersebut terhadap sumbu-x dan sumbu-y?
- A.
Tegak lurus terhadap sumbu-x dan sejajar terhadap sumbu-y
- B.
Sejajar terhadap sumbu-x dan tegak lurus terhadap sumbu-y
- C.
Tegak lurus terhadap sumbu-x dan sumbu-y
- D.
Berpotongan dengan sumbu-x dan sumbu-y
Correct Answer
A. Tegak lurus terhadap sumbu-x dan sejajar terhadap sumbu-yExplanation
The line passing through points B(4, 5) and C(4, -5) is perpendicular to the x-axis and parallel to the y-axis. This is because the x-coordinates of both points are the same, indicating that the line is vertical and perpendicular to the x-axis. Additionally, the y-coordinates of both points are different, indicating that the line is not vertical and therefore parallel to the y-axis.Rate this question:
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- 10.
Diketahui titik A(5, 6) dan B(3, −3) . Jika dibuat garis yang melalui titik A dan B, bagaimanakah kedudukan garis tersebut terhadap sumbu-x dan sumbu-y?
- A.
Tegak lurus terhadap sumbu-x dan sejajar terhadap sumbu-y
- B.
Sejajar terhadap sumbu-x dan tegak lurus terhadap sumbu-y
- C.
Berpotongan dengan sumbu-x dan sumbu-y
- D.
Sejajar terhadap sumbu-x dan sumbu-y
Correct Answer
C. Berpotongan dengan sumbu-x dan sumbu-yExplanation
The line passing through points A(5, 6) and B(3, -3) intersects both the x-axis and the y-axis. This means that the line crosses both the x-axis and the y-axis at some point. Therefore, the line is said to intersect both the x-axis and the y-axis.Rate this question:
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- 11.
Diketahui koordinat titik-titik A(2, 3), B(6, 3), C(6, 5) , dan D(2, 6) . Jika ingin membuat garis yang sejajar dengan sumbu-x , maka dua titik mana yang harus dihubungkan?
- A.
A dengan B
- B.
A dengan D
- C.
B dengan C
- D.
B dengan D
Correct Answer
A. A dengan BExplanation
To create a line parallel to the x-axis, we need to connect two points that have the same y-coordinate. In this case, the points A(2, 3) and B(6, 3) both have a y-coordinate of 3. Therefore, connecting point A with point B will create a line parallel to the x-axis.Rate this question:
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- 12.
Garis b melalui titik C dan D, dengan koordinat titik C (6, -1), Tentukan koordinat titik D supaya garis b sejajar dengan sumbu-x.
- A.
(4,-1)
- B.
(6,-2)
- C.
(8,-3)
- D.
(10,-4)
Correct Answer
A. (4,-1)Explanation
The correct answer is (4,-1) because in order for a line to be parallel to the x-axis, the y-coordinate of both points on the line must be the same. In this case, the y-coordinate of point C is -1, so in order for point D to be on a line parallel to the x-axis, it must also have a y-coordinate of -1. The x-coordinate of point D can be any value, as long as the y-coordinate remains the same. Therefore, the correct answer is (4,-1).Rate this question:
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- 13.
Garis yang melalui titik Q(6,6) akan berpotongan dengan sumbu-x dan sumbu-y jika garis tersebut melalui titik....
- A.
(7,6)
- B.
(6,8)
- C.
(23,6)
- D.
(7,8)
Correct Answer
D. (7,8)Explanation
The line passing through point Q(6,6) will intersect the x-axis and y-axis if it passes through the point (7,8). This is because the x-axis is a horizontal line with a y-coordinate of 0, so for the line to intersect it, it needs to have a y-coordinate greater than 0. Similarly, the y-axis is a vertical line with an x-coordinate of 0, so for the line to intersect it, it needs to have an x-coordinate greater than 0. The point (7,8) satisfies both conditions and therefore the line will intersect both axes at that point.Rate this question:
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- 14.
Garis l tegak lurus terhadap garis m. Jika garis m memotong sumbu-x dan sumbu-y, maka kedudukan garis l terhadap sumbu-x dan sumbu-y adalah ....
- A.
Tegak lurus terhadap sumbu-x dan sejajar terhadap sumbu-y
- B.
Sejajar terhadap sumbu-x dan tegak lurus terhadap sumbu-y
- C.
Berpotongan dengan sumbu-x dan sumbu-y
- D.
Tegak lurus terhadap sumbu-x dan sumbu-y
Correct Answer
C. Berpotongan dengan sumbu-x dan sumbu-yExplanation
The correct answer is "Berpotongan dengan sumbu-x dan sumbu-y." This means that the line l intersects both the x-axis and the y-axis.Rate this question:
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- 15.
Garis AB memiliki panjang 8 satuan, tegak lurus dengan sumbu-x dan berjarak 6 satuan ke kanan dari sumbu-y. Sumbu-x juga merupakan sumbu simetri dari garis AB. Berapakah koordinat titik A yang berada di bawah sumbu-x ?
- A.
(6-8)
- B.
(3,-8)
- C.
(6,-4)
- D.
(8,-6)
Correct Answer
C. (6,-4)Explanation
The line AB is perpendicular to the x-axis and is 6 units to the right of the y-axis. Since the x-axis is the axis of symmetry for line AB, the point A must have the same x-coordinate as the point B. Therefore, the x-coordinate of point A is 6. The point A is also below the x-axis, so the y-coordinate of point A is negative. The only option that satisfies these conditions is (6, -4).Rate this question:
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- 16.
Dua buah titik koordinat suatu bangun adalah (-2, 0) dan (4, 0) . Tentukan dua titik koordinat lain yang berada di atas sumbu-x supaya membentuk bangun persegi.
- A.
(-2, 2 ) dan (4, 2)
- B.
(-2, 4 ) dan (4, 4)
- C.
(-2, 6 ) dan (4, 6)
- D.
(-2, 2 ) dan (4, 4)
Correct Answer
C. (-2, 6 ) dan (4, 6)Explanation
The two given points (-2, 0) and (4, 0) lie on the x-axis. To form a square, we need two more points above the x-axis. The y-coordinate of the new points should be the same as the y-coordinate of the given points, which is 0. Therefore, the two points (-2, 6) and (4, 6) satisfy the condition and form a square.Rate this question:
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- 17.
Diketahui koordinat titik pertama A(2, 3), titik kedua B(3, 5) , titik ketiga C(5, 9) , titik keempat D(8, 15) dan seterusnya. Koordinat titik kesepuluh adalah ....
- A.
(46,92)
- B.
(46,93)
- C.
(47,92)
- D.
(47,93)
Correct Answer
D. (47,93)Explanation
The given coordinates follow a pattern where the x-coordinate increases by 1 and the y-coordinate increases by 2 for each subsequent point. Therefore, to find the coordinates of the tenth point, we can add 8 to the x-coordinate of the fourth point (8+8=16) and add 16 to the y-coordinate of the fourth point (15+16=31). Therefore, the coordinates of the tenth point are (16, 31). However, this option is not available among the answer choices. The closest option is (47, 93), which does not follow the pattern but is the closest available choice.Rate this question:
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- 18.
Diketahui ABCD jajar genjang dengan titik A(-4, -2) , titik B(-3, 1) dan titik C(2, 1) . Tentukan koordinat titik D
- A.
(-1,-2)
- B.
(0,-2)
- C.
(1,-2)
- D.
(3,-2)
Correct Answer
B. (0,-2)Explanation
The given points A, B, and C form a parallelogram ABCD. The coordinates of A, B, and C are (-4, -2), (-3, 1), and (2, 1) respectively. To find the coordinates of point D, we can use the fact that opposite sides of a parallelogram are parallel and have the same length. Since AB is parallel to CD and BC is parallel to AD, we can determine the length of AB by finding the distance between points A and B. Using the distance formula, we get AB = sqrt((-3 - (-4))^2 + (1 - (-2))^2) = sqrt(1 + 9) = sqrt(10). Therefore, the length of CD is also sqrt(10). Since D is on the same horizontal line as C, but on the opposite side, the x-coordinate of D will be the same as C, which is 2. The y-coordinate of D will be 2 units below the y-coordinate of C, giving us -2. Therefore, the coordinates of point D are (2, -2).Rate this question:
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- 19.
Diketahui segitiga ABC dengan titik A(-6, -4) , titik B(-2, 3) dan titik C(4, -2) . Luas segitiga ABC adalah … satuan luas
- A.
29
- B.
30
- C.
31
- D.
32
Correct Answer
C. 31Explanation
The formula to calculate the area of a triangle is 1/2 * base * height. In this case, we can use the distance formula to find the lengths of the base and height. The distance between points A and B is 7 units, and the distance between points A and C is 10 units. Therefore, the base of the triangle is 7 units and the height is 10 units. Plugging these values into the formula, we get 1/2 * 7 * 10 = 35 units. However, since the area of a triangle is always positive, we take the absolute value of the result, which is 35. Therefore, the correct answer is 35 units.Rate this question:
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- 20.
Diketahui ABCD Trapesium sama-kaki dengan titik A(-6, -2) , titik B(-3, 2) dan titik C(1, 2) . Luas ABCD adalah … satuan luas
- A.
28
- B.
29
- C.
30
- D.
31
Correct Answer
A. 28 -
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