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 [tex]\overline {AC}[/tex] = The length of [tex]\overline {BD}[/tex]
The length of [tex]\overline {AB}[/tex] = √((-10 - (-7))² + (-4 - (-8))²)) = 5
The length of [tex]\overline {CD}[/tex] = √((-5 - (-2))² + (-4 - (-8))²)) = 5
∴ The length of [tex]\overline {AB}[/tex] = The length of [tex]\overline {CD}[/tex]
[tex]\overline {AC}[/tex] is parallel to the horizontal axis
[tex]\overline {BD}[/tex] is parallel to the horizontal axis
∴ [tex]\overline {AC}[/tex] ║ [tex]\overline {BD}[/tex]
Given that [tex]\overline {AB}[/tex] = [tex]\overline {CD}[/tex], then [tex]\overline {AB}[/tex] ║ [tex]\overline {CD}[/tex]
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.)
