Question 37 Answer and Explanation _ACT July 2020 Form C01 Math Section

Use the following information to answer question 35-38.

In parallelogram ABCD shown below, the diagonals intersect at E, m∠BDC = 42°, m∠BDA = 71°, and AB= $\left({\frac{2}{3}n-5}\right)$ inches.

(Note: The figure is NOT drawn to scale; m∠PQR denotes the measure of ∠PQR.)

37. Suppose A and C are located at (2, 10) and (30, 3), respectively, in the standard (x, y) coordinate plane. What are the coordinates of E ?

A. $\left({-\frac{7}{2},\,14}\right)$

B. $\left({\frac{13}{2},\,16}\right)$

C. $\left({14,\,-\frac{7}{2}}\right)$

D. $\left({14,\,\frac{7}{2}}\right)$

E. $\left({16,\,\frac{13}{2}}\right)$

Answer and Explanation

Your Answer is

Correct Answer is E

Explanation

The horizontal and vertical coordinates of the key coordinates are the average of the horizontal and vertical coordinates of the two points AC.

Abscissa: (2+30)÷2 = 16

Vertical coordinate: (10+3)÷2 = 13/2