1.
In the standard (x,y) coordinate plane below, the points (0,2), (8,2), (3,6) and (11,6) are teh vertices of a parallelogram. What ist he area, in square units, of the parallelogram?
Correct Answer
C. 32
Explanation
The given points form a parallelogram in the coordinate plane. To find the area of a parallelogram, we can use the formula: base x height. The base of the parallelogram is the distance between the points (0,2) and (8,2), which is 8 units. The height of the parallelogram is the distance between the points (0,2) and (3,6), which is 4 units. Therefore, the area of the parallelogram is 8 x 4 = 32 square units.
2.
What is the approximate distance between the points (4, -3) and (-6, 5) in the standard (x, y) coordinate plane?
Correct Answer
B. 12.81
Explanation
The approximate distance between two points in a coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. The distance formula is given by:
d = âˆš((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the two points are (4, -3) and (-6, 5). Plugging these values into the distance formula, we get:
d = âˆš((-6 - 4)^2 + (5 - (-3))^2)
= âˆš((-10)^2 + (8)^2)
= âˆš(100 + 64)
= âˆš(164)
â‰ˆ 12.81
Therefore, the approximate distance between the two points is 12.81.
3.
Given the vertices of parallelogram FGHJ in the standard (x, y) coordinate plane below, what is the area of triangle GHJ in square units?
Correct Answer
C. 22
Explanation
To find the area of triangle GHJ, we need to calculate the base and height of the triangle. The base is the distance between points G and H, which can be found using the distance formula. The height is the distance between the line containing points G and H and point J, which can be found by calculating the perpendicular distance from point J to the line containing points G and H. Once we have the base and height, we can use the formula for the area of a triangle (1/2 * base * height) to find the area.
4.
In the figure above, OS = ST and the coordinates of T are (k, 5). What is the value of k?
Correct Answer
E. 5
Explanation
In the figure, it is given that OS = ST, which means that the length of OS is equal to the length of ST. The coordinates of T are given as (k, 5). Since OS = ST, the y-coordinate of T should also be 5. Therefore, the value of k should be such that the point T has a y-coordinate of 5. Looking at the answer options, the only value that satisfies this condition is k = 5.
5.
What is the slope of a line that is perpendicular to the line determined by the equation 5x + 8y = 17?
Correct Answer
E. 8/5
Explanation
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. The given equation can be rewritten in slope-intercept form as y = (-5/8)x + 17/8. Therefore, the slope of the original line is -5/8. The negative reciprocal of -5/8 is 8/5, which is the slope of the line perpendicular to the given line.
6.
In the standard (x, y) coordinate plane shown below, what is the distance on the y-axis, in units, from point A to point B?
Correct Answer
D. 5
Explanation
The distance on the y-axis from point A to point B is 5 units. This can be determined by subtracting the y-coordinate of point A from the y-coordinate of point B, which gives a difference of 5.
7.
An overlay of an accessibility ramp of a building is placed on the standard (x,y) coordinate plane so that the x-axis aligns with the horizontal. The line segment representing the side view of the ramp goes through the point (-2, -1) and (16, 2). What is the slope of the accessibility ramp?
Correct Answer
D. 1/6
Explanation
The slope of a line can be found by calculating the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, the change in y-coordinates is 2 - (-1) = 3, and the change in x-coordinates is 16 - (-2) = 18. Therefore, the slope of the accessibility ramp is 3/18, which simplifies to 1/6.
8.
In the standard (x, y) coordinate plane, point B with coordinates (5, 6) is the midpoint of AC, and A has coordinates (6, 7). What are the coordinates of C?
Correct Answer
C. (4, 5)
Explanation
Since point B is the midpoint of AC, the coordinates of point C can be found by using the midpoint formula. The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. In this case, the x-coordinate of point C is (6 + x) / 2 = 5, which gives x = 4. Similarly, the y-coordinate of point C is (7 + y) / 2 = 6, which gives y = 5. Therefore, the coordinates of point C are (4, 5).
9.
In the square graphed below, what is the slope of the line segment AC?
Correct Answer
C. 1
Explanation
The slope of a line segment can be determined by finding the change in the y-coordinates divided by the change in the x-coordinates. In this case, the line segment AC goes from point A to point C, which has a change in y-coordinate of 2 and a change in x-coordinate of 2. Therefore, the slope of the line segment AC is 2/2 = 1.
10.
Which of the following is the slope of a line parallel to the line y = 2/5x + 7 in the standard (x, y) plane?
Correct Answer
C. 2/5
Explanation
The slope of a line parallel to another line will have the same slope. In this case, the given line has a slope of 2/5. Therefore, the slope of a line parallel to it will also be 2/5.
11.
Quadrilateral QRST is shown below in the standard (x, y) coordinate plane.What is the length of QS in coordinate units?
Correct Answer
A. A
12.
Which of the following is closest to the perimeter of quadrilateral QRST, in coordinate units?
Correct Answer
C. 19.8
13.
What is the slope-intercept form of 10x - y - 8 = 0?
Correct Answer
D. Y = 10x - 8
Explanation
The given equation is in the form of Ax + By + C = 0. To convert it to slope-intercept form (y = mx + b), we need to isolate y. By rearranging the equation, we get y = 10x - 8. Therefore, the correct answer is y = 10x - 8.
14.
What is the distance in standard (x, y) coordinate plane between the points (5, 5) and (1, 0)?
Correct Answer
B. B
Explanation
The distance between two points in a standard (x, y) coordinate plane can be calculated using the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates of the two points. In this case, the x-coordinate difference is 5-1=4 and the y-coordinate difference is 5-0=5. Therefore, the distance is the square root of (4^2 + 5^2) = square root of (16 + 25) = square root of 41.
15.
What is the slope of the line determined by the equation 2x - 3y = 6?
Correct Answer
D. 2/3
Explanation
The slope of a line can be determined by rearranging the equation into slope-intercept form, y = mx + b, where m represents the slope. In this case, rearranging 2x - 3y = 6 gives -3y = -2x + 6, then dividing by -3 yields y = (2/3)x - 2. Therefore, the slope of the line is 2/3.