Question

show that the points (-4,0),(4,0) and (0,3) are vertices of an isosceles triangle.

Answer 1

the distance b/w points (-4,0)&(4,0)= √[{ 4-(-4)}²+(0-0)²]=√8²= 8
the distance b/w points (4,0)&(0,3)= √[(4-0)²+(0-3)²]=√(16+9)= 5
the distance b/w the points (0,3)&(-4,0)=√[(0-(-4))²+(3-0)²= √( 16+9)= 5
the two distances are equal that is two sides of the triangle are equal so the triangle is isosceles.

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let X (- 4, 0), Y (4, 0) and Z(0, 3) are the given vertices.

Now, distance between X( - 4, 0) and Y(4, 0),

⇒ XY = √[4 - (- 4)]² + (0 - 0)²

⇒ XY = √(4 - 4)²

⇒ XY = √(8)²

⇒ XY = 8

Distance between Y(4, 0) and Z(0, 3),

⇒ YZ = √(0 - 4)² + (3 - 0)²

⇒ YZ = √16 + 9

⇒ YZ = √25

⇒ YZ = 5

Distance between Z(4, 0) and X(0, 3)

⇒ ZX = √[0 - (- 4)]² + (3 - 0)²

⇒ ZX = √16 + 9

⇒ ZX = √25

⇒ ZX = 5

As, YZ = ZX

Two sides of the triangle are equal.

So that, the triangle XYZ is an isosceles triangle.