Question

1. Name the type of triangle formed by the points A (-5, 6), B (-4,-2) and C (7, 5).​

Answer 1

Answer:

Scalene Triangle

Step-by-step explanation:

A (–5, 6), B (–4, –2) and C (7, 5)

AB = √{(-4+5)² + (-2-6)²}

= √1+64

=√65

BC=√{(7+4)² + (5+2)²}

=√121 + 49

=√170

AC=√{(7+5)² + (5-6)²}

=√144 + 1

=√145

Note: The formula used is

Distance d= √{(X2 - X1)² + (Y2- Y1)²}

All sides are different in measure, so ABC is a scalene triangle.

Hope it helps if so please mark as brainliest, please.

Answer 2

$\huge\bold\blue{Solution:-}$

$\huge{\underline{\underline{\mathsf{\pink{Given}}}}}:-$

Coordinate of A (-5,6)

Coordinate of B (-4,7)

Coordinate of (7,5)

Finding sides of ∆ by distance formula:-

|AB| = $\sqrt{(7-6)^2 +(-4+5)^2}$

→ $\sqrt{1+1}$

→ $\sqrt{2}$

|AC| = $\sqrt{(5-6)^2+(7+5)^2}$

→ $\sqrt{1+12}$

→ $\sqrt{13}$

|BC| = $\sqrt{(5-7)^2+(7+4)^2}$

→ $\sqrt{4+11}$

→ $\sqrt{15}$

† Here, AB, ≠ AC ≠ BC

${\underline{\underline{\mathsf{\red{ Hence, \ triangle \ ABC \ is \ scalene }}}}}$

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