Question

Show that A (-3, o) B (1, -3) and C (4, 1) are the vertices of an isosceles right angled
triangle . Also find the area of the triangle.​

Answer 1

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Show that A (-3, o) B (1, -3) and C (4, 1) are the vertices of an isosceles right angled

triangle . Also find the area of the triangle.

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now ...A (-3, o) B (1, -3) and C (4, 1)

therefore...AB

$= \sqrt{( - 3 - 1) {}^{2} + (0 + 3) {}^{2} } \\ = \sqrt{25} \\ = 5$

BC

$= \sqrt{(1 - 4) {}^{2} + ( - 3 - 1) {}^{2} } \\ = \sqrt{25} \\ = 5$

CA

$\sqrt{(4 + 3) {}^{2} + (1 - 0) {}^{2} } \\ = \sqrt{50} \\ = 5 \sqrt{2}$

as the two sides are equal so ...the triangle ∆ABC is a isosceles triangle ...

(2)

A (-3, o) B (1, -3) and C (4, 1)

now area of the ∆ABC

is ...

$= \frac{1}{2} ( - 3( - 3 - 1) + 1(1 - 0) + 4(0 + 3)) \\ = \frac{1}{2} ( + 12 + 1 + 12) \\ = 12.5 \: \: unit {}^{2}$

$\huge\mathcal\green{\underline{hope\:\: this\:\: helps\:\: you}}$