Question

Given W(9,8),X(8,3),Y(2,5) and Z(x,0). Find x such that segment WX is paralell to segment YZ

Answer 1

The value of x is 1 to make segment WX parallel to segment YZ. This is found by ensuring both segments have the same slope, which is a key property of parallel lines.

Step-by-step explanation:

To determine the value of x such that segment WX is parallel to segment YZ, you need to ensure that the slopes of these two segments are equal. The slope is calculated by the change in the y-coordinates divided by the change in the x-coordinates of the endpoints of the segments.

First calculate the slope of WX:

mWX = (y2 - y1) / (x2 - x1)
= (3 - 8) / (8 - 9)
= -5 / -1
= 5

Since we need WX to be parallel to YZ, we need their slopes to be equal. Let's apply this to YZ:

mYZ = (0 - 5) / (x - 2)
= -5 / (x - 2)

To have WX parallel to YZ, set mWX = mYZ:

5 = -5 / (x - 2)

After cross multiplying, we have:

5(x - 2) = -5
5x - 10 = -5
5x = 5
x = 1

The value of x is 1 for segment WX to be parallel to segment YZ.