First slide

Cartesian plane

Question

The points $(- 3, 1), (- 6, - 7), (3, - 9), (6, - 1)$ are

Easy

A

Vertices of a rectangle
B

Collinear
C

Vertices of a parallelogram
D

Vertices of a rhombus

Solution

$A (- 3, 1), B (- 6, - 7), C (3, - 9), D (6, - 1)$
$A + C = B + D$

$\overset{\leftrightarrow}{A B}$ slope $= \frac{- 8}{3}$

$\overset{\leftrightarrow}{B C}$ slope $= \frac{- 2}{9}$

$\bar{A B} = \sqrt{9 + 64} = \sqrt{73}, B C = \sqrt{81 + 4} = \sqrt{85}$

$A B \neq B C \Rightarrow$ A,B,C,D forms a parallelogram

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