Question

What is the strongest classification of the figure formed by the following points?

Answer 1

Answer:

A. Parallelogram

Step-by-step explanation:

The given points are;

(-10, -4), (-7, -8), (-5, -4), (-2, -8)

Let 'A' represent the point (-10, -4), let 'B' represent the point (-7, -8), let 'C' represent the point (-5, -4), and let 'D' represent the point (-2, -8), we have;

The (horizontal) distance between points A and C = -5 - (-10) = 5

The (horizontal) distance between points B and D = -2 - (-7) = 5

Therefore;

The length of $\overline {AC}$ = The length of $\overline {BD}$

The length of $\overline {AB}$ = √((-10 - (-7))² + (-4 - (-8))²)) = 5

The length of $\overline {CD}$ = √((-5 - (-2))² + (-4 - (-8))²)) = 5

∴ The length of $\overline {AB}$ = The length of $\overline {CD}$

$\overline {AC}$ is parallel to the horizontal axis

$\overline {BD}$ is parallel to the horizontal axis

∴ $\overline {AC}$ ║ $\overline {BD}$

Given that $\overline {AB}$ = $\overline {CD}$, then $\overline {AB}$ ║ $\overline {CD}$

Therefore, the quadrilateral ABCD is a parallelogram

(The angle ∠ABD = 180 - arctan (4/3) ≈ 126.9 > 90, therefore, the parallelogram ABCD is not a rectangle.)