Question

The vertices of AWXY are W(-4,1), X(0, -5), and Y(4, -1). A is the midpoint of

WY, and B is the midpoint of XY. Show that AB ||WX and AB = WX.

Answer 1

To show that AB || WX, we need to prove that the slopes of AB and WX are equal. We can do this by finding the equations of AB and WX and comparing their slopes. To prove that AB = WX, we need to find the lengths of AB and WX using the distance formula.

Step-by-step explanation:

To show that AB || WX, we need to prove that the slopes of AB and WX are equal. Let's find the equations of AB and WX using the given coordinates.

The midpoint of WY is A((-4+4)/2, (1-1)/2) = A(0,0). The midpoint of XY is B((0+4)/2, (-5-1)/2) = B(2, -3).

The equation of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula: (y-y1)/(y2-y1) = (x-x1)/(x2-x1).

The equation of AB is (y-0)/(-3-0) = (x-0)/(2-0), which simplifies to y = -3/2x.

The equation of WX is (y-1)/(-5-1) = (x+4)/0, which simplifies to x = -4.

Comparing the slopes, we can see that the slope of AB is -3/2 and the slope of WX is 0. Since the slopes are not equal, AB is not parallel to WX.

To prove that AB = WX, we need to find the lengths of AB and WX using the distance formula.

The length of AB can be found using the distance formula: AB = sqrt((2-0)^2 + (-3-0)^2) = sqrt(4+9) = sqrt(13).

The length of WX can be found by calculating the difference in their x-coordinates: WX = |0 - (-4)| = 4.

Since AB = sqrt(13) and WX = 4, AB is not equal to WX. Therefore, AB neither parallel nor equal to WX.