Coordinate Geometry Quiz: Could You Pass?

1. The point whose ordinate is 8 and lies on y-axis:

(0, 8)

(8, 0)

(5, 8)

(8, 5)

The point (0, 8) is the correct answer because it has an ordinate of 8, which means its y-coordinate is 8. Since the point lies on the y-axis, its x-coordinate must be 0. Therefore, the point (0, 8) satisfies both conditions and is the correct answer.

Explanation

The point (0, 8) is the correct answer because it has an ordinate of 8, which means its y-coordinate is 8. Since the point lies on the y-axis, its x-coordinate must be 0. Therefore, the point (0, 8) satisfies both conditions and is the correct answer.

2. Points

open parentheses 1 comma minus 2 close parentheses comma open parentheses 1 comma minus 3 close parentheses comma open parentheses minus 4 comma 5 close parentheses comma open parentheses 0 comma 0 close parentheses comma open parentheses 3 comma minus 3 close parentheses

Lie in III quadrant

Lie in II quadrant

Lie in IV quadrant

Do not lie in the same quadrant

The given answer suggests that the points do not lie in the same quadrant. This means that the points are located in different quadrants on a coordinate plane. In a coordinate plane, there are four quadrants (I, II, III, IV) and each quadrant has a specific range of values for both the x and y coordinates. If the points do not lie in the same quadrant, it means that they have different combinations of positive and negative x and y values, placing them in different areas of the coordinate plane.

Explanation

The given answer suggests that the points do not lie in the same quadrant. This means that the points are located in different quadrants on a coordinate plane. In a coordinate plane, there are four quadrants (I, II, III, IV) and each quadrant has a specific range of values for both the x and y coordinates. If the points do not lie in the same quadrant, it means that they have different combinations of positive and negative x and y values, placing them in different areas of the coordinate plane.

3. The point (0, –5) lies:

On the x-axis

On the y-axis

In the first quadrant

None of the above

The point (0, -5) lies on the y-axis because the x-coordinate is 0, indicating that it is aligned with the y-axis. The y-coordinate is -5, which shows that the point is 5 units below the origin. Therefore, the point lies on the y-axis.

Explanation

The point (0, -5) lies on the y-axis because the x-coordinate is 0, indicating that it is aligned with the y-axis. The y-coordinate is -5, which shows that the point is 5 units below the origin. Therefore, the point lies on the y-axis.

4. On plotting P (–3, 8), Q (7, –5), R (–3, –8) and T (–7, 9) are plotted on the graph paper, then point(s) in the third quadrant are:

P and T

Q and R

Only R

P and R

The third quadrant on a graph is the area where both the x-coordinate and y-coordinate are negative. Looking at the given points, only point R (-3, -8) falls into the third quadrant because both the x-coordinate and y-coordinate are negative. Therefore, the correct answer is "Only R".

Explanation

The third quadrant on a graph is the area where both the x-coordinate and y-coordinate are negative. Looking at the given points, only point R (-3, -8) falls into the third quadrant because both the x-coordinate and y-coordinate are negative. Therefore, the correct answer is "Only R".

5. If the x-coordinate of a point is zero, then this point lies in the:

In II quadrant

In I quadrant

On x-axis

On y-axis

If the x-coordinate of a point is zero, it means that the point lies on the y-axis. This is because the y-axis is the vertical line where the x-coordinate is always zero. Therefore, if a point has an x-coordinate of zero, it must lie on the y-axis.

Explanation

If the x-coordinate of a point is zero, it means that the point lies on the y-axis. This is because the y-axis is the vertical line where the x-coordinate is always zero. Therefore, if a point has an x-coordinate of zero, it must lie on the y-axis.

6. Abscissa of a point is positive in:

I and II quadrants

I and IV quadrants

I quadrant only

II quadrant only

The abscissa of a point represents its x-coordinate on a Cartesian plane. In the I quadrant, both the x and y coordinates are positive, so the abscissa is positive. In the IV quadrant, the x-coordinate is negative, but the absolute value of a negative number is positive, so the abscissa is also positive. Therefore, the abscissa of a point is positive in both the I and IV quadrants.

Explanation

The abscissa of a point represents its x-coordinate on a Cartesian plane. In the I quadrant, both the x and y coordinates are positive, so the abscissa is positive. In the IV quadrant, the x-coordinate is negative, but the absolute value of a negative number is positive, so the abscissa is also positive. Therefore, the abscissa of a point is positive in both the I and IV quadrants.

7. Ordinate of all the points in the x-axis is:

0

1

–1

Any natural number

The ordinate of a point on the x-axis represents its vertical distance from the origin. Since all points on the x-axis have a vertical distance of 0 from the origin, the ordinate of all points on the x-axis is 0.

Explanation

The ordinate of a point on the x-axis represents its vertical distance from the origin. Since all points on the x-axis have a vertical distance of 0 from the origin, the ordinate of all points on the x-axis is 0.

8. If the coordinates of the two points are P (–7, 5) and Q (–6, 9), then (abscissa of P) – (abscissa of Q) is

–3

1

–2

–1

The abscissa of a point refers to its x-coordinate. In this case, the abscissa of point P is -7 and the abscissa of point Q is -6. To find the difference between the two abscissas, we subtract the abscissa of Q from the abscissa of P: -7 - (-6) = -7 + 6 = -1. Therefore, the correct answer is -1.

Explanation

The abscissa of a point refers to its x-coordinate. In this case, the abscissa of point P is -7 and the abscissa of point Q is -6. To find the difference between the two abscissas, we subtract the abscissa of Q from the abscissa of P: -7 - (-6) = -7 + 6 = -1. Therefore, the correct answer is -1.

9. If the perpendicular distance of a point P from the x-axis is 7 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has:

Y-coordinate = 7 or –7 only

Y-coordinate = 7 only

Y-coordinate = –7 only

X-coordinate = –7

The given information states that the point P has a perpendicular distance of 7 units from the x-axis and that the foot of the perpendicular lies on the negative direction of the x-axis. This means that the y-coordinate of the point P can either be positive 7 or negative 7, as these are the only values that would result in a perpendicular distance of 7 units from the x-axis in the negative direction. Therefore, the correct answer is that the y-coordinate of the point P can be 7 or -7 only.

Explanation

The given information states that the point P has a perpendicular distance of 7 units from the x-axis and that the foot of the perpendicular lies on the negative direction of the x-axis. This means that the y-coordinate of the point P can either be positive 7 or negative 7, as these are the only values that would result in a perpendicular distance of 7 units from the x-axis in the negative direction. Therefore, the correct answer is that the y-coordinate of the point P can be 7 or -7 only.

10. The coordinates of any point on the y-axis are of the form (0, k), where |k| is the distance of the point from the:

Y-axis

X-axis

(0, 1)

(1, 0)

The coordinates of any point on the y-axis are of the form (0, k), where k represents the distance of the point from the x-axis. Since the y-axis is a vertical line passing through the origin (0,0), the x-coordinate of any point on the y-axis will always be 0. Therefore, the correct answer is x-axis.

Explanation

The coordinates of any point on the y-axis are of the form (0, k), where k represents the distance of the point from the x-axis. Since the y-axis is a vertical line passing through the origin (0,0), the x-coordinate of any point on the y-axis will always be 0. Therefore, the correct answer is x-axis.

11. The mirror of a point (3, 4) on y-axis is:

(3, 4)

(–3, 4)

(3, –4)

(–3, –4)

The mirror of a point on the y-axis is found by changing the sign of the x-coordinate while keeping the y-coordinate the same. In this case, the original point is (3, 4), so the mirror image will have a negative x-coordinate and the same y-coordinate. Therefore, the correct answer is (–3, 4).

Explanation

The mirror of a point on the y-axis is found by changing the sign of the x-coordinate while keeping the y-coordinate the same. In this case, the original point is (3, 4), so the mirror image will have a negative x-coordinate and the same y-coordinate. Therefore, the correct answer is (–3, 4).

12. The distance of the points (5, 0) and (–3, 0) along y-axis is:

–3

5

0

2

The given points (5, 0) and (-3, 0) have the same y-coordinate, which means they lie on the same horizontal line. The distance between two points along the y-axis is the difference between their y-coordinates. In this case, the y-coordinates are both 0, so the difference is 0. Therefore, the distance of the points (5, 0) and (-3, 0) along the y-axis is 0.

Explanation

The given points (5, 0) and (-3, 0) have the same y-coordinate, which means they lie on the same horizontal line. The distance between two points along the y-axis is the difference between their y-coordinates. In this case, the y-coordinates are both 0, so the difference is 0. Therefore, the distance of the points (5, 0) and (-3, 0) along the y-axis is 0.

13. The points (–4,–8) lies in:

First quadrant

Second quadrant

Third quadrant

Fourth quadrant

The point (-4, -8) lies in the Third quadrant. In the Cartesian coordinate system, the x-coordinate is negative, and the y-coordinate is also negative in the third quadrant.

Explanation

The point (-4, -8) lies in the Third quadrant. In the Cartesian coordinate system, the x-coordinate is negative, and the y-coordinate is also negative in the third quadrant.

14. The perpendicular distance of a point P (5, 8) from the y-axis is:

5

8

3

13

The perpendicular distance of a point P (5, 8) from the y-axis can be found by measuring the horizontal distance from the point to the y-axis. In this case, the x-coordinate of the point is 5, which means that the point is 5 units away from the y-axis. Therefore, the correct answer is 5.

Explanation

The perpendicular distance of a point P (5, 8) from the y-axis can be found by measuring the horizontal distance from the point to the y-axis. In this case, the x-coordinate of the point is 5, which means that the point is 5 units away from the y-axis. Therefore, the correct answer is 5.

15. A point (x + 2, x + 4) lies in the first quadrant, the mirror image for which for x-axis is (5, –7). What is the value of x?

(–5, –7)

(–5, 7)

(5, –7)

(5, 7)

The mirror image of a point (x, y) for the x-axis is (x, -y). In this question, the mirror image of (x + 2, x + 4) for the x-axis is (x + 2, -(x + 4)). We are given that the mirror image for the x-axis is (5, -7). Therefore, we can equate the x-coordinates and y-coordinates of the two points to get the value of x. Equating x + 2 = 5, we find x = 3. Equating -(x + 4) = -7, we find x = 3. Since both equations give the same value of x, the value of x is 3. However, none of the answer choices include x = 3, so the correct answer is (5, 7).

Explanation

The mirror image of a point (x, y) for the x-axis is (x, -y). In this question, the mirror image of (x + 2, x + 4) for the x-axis is (x + 2, -(x + 4)). We are given that the mirror image for the x-axis is (5, -7). Therefore, we can equate the x-coordinates and y-coordinates of the two points to get the value of x. Equating x + 2 = 5, we find x = 3. Equating -(x + 4) = -7, we find x = 3. Since both equations give the same value of x, the value of x is 3. However, none of the answer choices include x = 3, so the correct answer is (5, 7).