Question

If the points A(-3,1),B(-6,-7),C(3,9),D(6,-1) forms a ​

Answer 1

CORRECTION: IT IS C(3, -9), not (3,9).

$\mathcal{\green{\underline{\blue{GIVEN:}}}}$

• We are given four points:  A(-3,1),B(-6,-7),C(3,-9),D(6,-1).

$\mathcal{\green{\underline{\blue{TO \:\: FIND:}}}}$

• We need to find what shape does the points form.

$\mathcal{\green{\underline{\blue{SOLUTION:}}}}$

We need to use the distance formula, which goes as:

$d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$

• The distance of AB:

$d = \sqrt {(-6 - (-3))^2 + (-7 - 1)^2}$

$d=\sqrt{73} \:\: units.$

• The distance of BC:

$d = \sqrt {(3 - (-6))^2 + (-9 - (-7))^2}$

$d=\sqrt{85} \:\: units.$

• The distance of CD:

$d = \sqrt {(6 - 3)^2 + (-1 -(- 9))^2}$

$d=\sqrt{73} \:\: units.$

• The distance of DA:

$d = \sqrt {(-3 - 6)^2 + (1 - (-1))^2}$

$d=85 \:\: units.$

Thus, AB=CD, BC=DA.

Opposite sides are equal, thus it is a parallelogram.

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