Question

I really need help with this homework If you could help me I would appreciate it very much please and thank you

Answer 1

Hello there. To solve this question, we'll have to remember some properties about coordinate geometry.

Given the following rectangle in the coordinate plane:

First, we determine the coordinates of the vertices A, B, C and D.

Notice that we can calculate its dimensions by simply calculating the distance between each vertex.

In this case, since we have a rectangle, the sides are pairwise congruent, which means that AB // DC and AD // BC and have the same measures.

The distance formula d(x,y) for two points (x0, y0) and (x1, y1) is given by:

`d(x,y)=√((x_1-x_0)^2+(y_1-y_0)^2)`

As suggested, we only have to measure two sides of it, hence choosing the sides AB and AD, we'll get

Determining the coordinates of A: it is the point (-4,4)

Determining the coordinates of B: it is the point (10, 4)

Determining the coordinates of D: it is the point (-4, -4)

Using the distance formula, we get

`\begin{gathered} d(AB)=√((-4-(10))^2+(4-4)^2)=√(14^2+0^2)=√(14^2)=14 \\ \\ d(AD)=√((-4-(-4))^2+(4-(-4))^2)=√(0^2+8^2)=√(8^2)=8 \\ \\ \end{gathered}`

Hence, we got

Its dimensions are given by

mAB x mAD = 14 units x 8 units.

This is the answer to this question and it is contained in the last option.