Question

show that the point (2,0),(-2,0)and(0,2) are the vertices of a triangle .also state with reason the type of the triangle​ by slope formula

Answer 1

Answer:

The given points form an isoceles right angled triangle.

Step-by-step explanation:

Formula used:

Slope of the line joining $(x_1,y_1)$ and $(x_2,y_2)$ is

$\frac{y_2-y_1}{x_2-x_1}$

Let the given points be A(2,0) B(-2,0) C(0,2).

Slope of AC

=$\frac{y_2-y_1}{x_2-x_1}$

Slope of AC

$=\frac{2-0}{0-2}$

Slope of AC

$=\frac{2}{-2}$

Slope of AC= -1

Slope of BC

$=\frac{y_2-y_1}{x_2-x_1}$

Slope of BC

$=\frac{2-0}{0+2}$

Slope of BC

$=\frac{2}{2}$

Slope of BC= 1

slope of AC$\neq$slope of BC

The given points are not collinear

Hence they form a triangle.

Slope of AC= -1

$tan\theta_1=-1$

$\theta_1=135$

Hence ∠A =45

Slope of BC= 1

$tan\theta_2=1$

$\theta_2=45$

Hence ∠B=45

∠A=∠B

Base angles are equal

Also ∠C=90

Therefore ΔABC is an isoceles right angled triangle.

Answer 2

Answer:

Isosceles right angled triangle

Step-by-step explanation:

Distance between

Side 1  (2,0) & (-2,0) = √((2-(-2))² + (0-0)²) = √ (4² + 0) = 4

Side 2 (2,0) & (0,2) = √((2-0)² + (0-2)²) = √ (4 + 4) = √8 = 2√2

Side 3 (-2,0) & (0,2) = √((-2-0)² + (0-2)²) = √ (4 + 4) = √8 =2√2

(√8)² + (√8)² = 4²

Side2² + Side3² = Side1²

Right angle triangle

2√2 = 2√2

Side 2 = Side 3

Isosceles right angled triangle