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:
[tex]d(x,y)=\sqrt{(x_1-x_0)^2+(y_1-y_0)^2}[/tex]
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
[tex]\begin{gathered} d(AB)=\sqrt{(-4-(10))^2+(4-4)^2}=\sqrt{14^2+0^2}=\sqrt{14^2}=14 \\ \\ d(AD)=\sqrt{(-4-(-4))^2+(4-(-4))^2}=\sqrt{0^2+8^2}=\sqrt{8^2}=8 \\ \\ \end{gathered}[/tex]
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.
