First slide

Equation of line in Straight lines

Question

The points $(3, - 2), (7, 6), (- 1, 2), (- 5, - 6)$ form

Moderate

A

A parallelogram
B

A rectangle
C

A rhombus
D

A square

Solution

$A (3, - 2), B (7, 6), C (- 1, 2), D (- 5, - 6)$
$\overset{\leftrightarrow}{A B}$ slope $= \frac{8}{4} = 2$

$\overset{\leftrightarrow}{B C}$ slope $= \frac{- 4}{- 8} = \frac{1}{2}$ $\overset{\leftrightarrow}{A B} ⊥_{r} \overset{\leftrightarrow}{B C}$

$A B = \sqrt{16 + 64} = \sqrt{80}$

$B C = \sqrt{64 + 16} = \sqrt{80}$ $\Rightarrow A B = B C$

$∴$ A, B, C, D forms a Rhombus

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