First slide

Cartesian plane

Question

The points $(8, 4), (5, 7), (- 1, 1), (2, - 2)$ form

Moderate

A

a parallelogram
B

a rectangle
C

a rhombus
D

a square

Solution

$A (8, 4), B (5, 7), C (- 1, 1), D (2, - 2)$
$A + C = B + D$

$\overset{\leftrightarrow}{A B}$ slope $= \frac{3}{- 3} = - 1$ $\overset{\leftrightarrow}{B C}$ $= \frac{- 6}{- 6} = 1$ $\overset{\leftrightarrow}{A B} ⊥ \overset{\leftrightarrow}{B C}$

$A B = \sqrt{9 + 9} = \sqrt{18}$

$B C = \sqrt{36 + 36} = \sqrt{72}$

$A B \neq B C$

$∴$ A,B,C,D form a rectangle

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