Coordinate Geometry Level 1

1) In the standard (x, y) coordinate plane, point X has coordinates (-4, 0) and point Y has coordinates (0, -8). What are the coordinates of the midpoint of XY?

(-6, -1)

(-2, -4)

(0, 2)

(2, 4)

(6, -1)

The midpoint of a line segment is the point that is exactly halfway between the two endpoints. To find the coordinates of the midpoint, we average the x-coordinates and the y-coordinates of the endpoints separately. In this case, the x-coordinate of the midpoint is (-4 + 0)/2 = -2, and the y-coordinate is (0 + (-8))/2 = -4. Therefore, the coordinates of the midpoint of XY are (-2, -4).

Explanation

The midpoint of a line segment is the point that is exactly halfway between the two endpoints. To find the coordinates of the midpoint, we average the x-coordinates and the y-coordinates of the endpoints separately. In this case, the x-coordinate of the midpoint is (-4 + 0)/2 = -2, and the y-coordinate is (0 + (-8))/2 = -4. Therefore, the coordinates of the midpoint of XY are (-2, -4).

2) Point A is to be graphed in a quadrant, not on an axis, of the standard (x, y) coordinate plane below. If the x-coordinate and the y-coordinate of point A are to have the same signs, then point A must be located in:

Quadrant I only

Quadrant II only

Quadrant III only

Quadrant I or II only

Quadrant I or III only

If the x-coordinate and the y-coordinate of point A are to have the same signs, it means that both coordinates will either be positive or negative. In Quadrant I, both x and y coordinates are positive, while in Quadrant III, both x and y coordinates are negative. Therefore, point A must be located in either Quadrant I or III only to satisfy the given condition.

Explanation

If the x-coordinate and the y-coordinate of point A are to have the same signs, it means that both coordinates will either be positive or negative. In Quadrant I, both x and y coordinates are positive, while in Quadrant III, both x and y coordinates are negative. Therefore, point A must be located in either Quadrant I or III only to satisfy the given condition.

3) In the standard (x, y) coordinate plane, what is the slope of the line joining the points (3, 7) and (4, -8)?

-15

-1

-1/7

21/32

15

The slope of a line is determined by the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. In this case, the change in y is -8 - 7 = -15 and the change in x is 4 - 3 = 1. Therefore, the slope is -15/1 = -15.

Explanation

The slope of a line is determined by the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. In this case, the change in y is -8 - 7 = -15 and the change in x is 4 - 3 = 1. Therefore, the slope is -15/1 = -15.