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Properties of Isosceles and Equilateral Triangles

Show that the...

Question

Show that the following points form an isosceles triangle.
(1, 3), (-3, -5) and (-3, 0)

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Solution

Given,
$A (1, 3), B (- 3, - 5), C (- 3, 0)$

$A B = \sqrt{(- 3 - 1)^{2} + (- 5 - 3)^{2}}$

$= \sqrt{80}$

$B C = \sqrt{(- 3 - (- 3))^{2} + 5^{2}} = 5$

$C A = \sqrt{4^{2} + 3^{2}} = 5$

$A B = B C$

Hence it is isoceles $Δ$

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