## VERTICES OF RIGHT TRIANGLE4

Vertices of right triangle4 :

Here we are going to see solution of the first question.

Question 4 :

Examine whether the given points  A (2,0) and B (-2,3) and C (-2,-5) forms a right triangle.

Solution :

To show that the given points forms a right triangle, we need to find the distance between three points. The sum of squares of two sides is equal to the square of remaining side.

Distance Between Two Points (x ₁, y₁) and (x₂ , y₂)

√(x₂ - x₁)² + (y₂ - y₁)²

The three points are  A (2,0) and B (-2,3) and C (-2,-5)

Distance between the points A and B

= √(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 2, y₁ = 0, x₂ = -2  and  y₂ = 3

=  √(-2-2))² + (3-0)²

=    √(-4)² + (3)²

=   √16 + 9

=   √25  units

Distance between the points B and C

= √(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = -2, y₁ = 3, x₂ = -2  and  y₂ = -5

=  √(-2-(-2))² + (-5-3)²

=    √(-2+2)² + (-8)²

=    √0² + 64

=    √64 units

Distance between the points C and A

= √(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = -2, y₁ = -5, x₂ = 2  and  y₂ = 0

=  √(2-(-2))² + (0-(-5))²

=   √(2+2)² + (0+5)²

=    √4² + (5)²

=    √16 + 25

=    √41 units

AB = √25 units

BC = √64 units

CA = √41 units

(BC)² = (AB)² + (CA)²

(√64)²  = (√25)² + (√41)²

64 = 25 + 41

64 ≠ 66

Hence, the given points A,B and C will not form a right triangle.

## Try other questions

(1)  Examine whether the given points  A (-3,-4) and B (2,6) and C(-6,10) forms a right triangle.

(2)  Examine whether the given points  P (7,1) and Q (-4,-1) and R (4,5) forms a right triangle.

(3)  Examine whether the given points  P (4,4) and Q (3,5) and R (-1,-1) forms a right triangle.

(4)  Examine whether the given points  A (2,0) and B (-2,3) and C (-2,-5) forms a right triangle.

(5)  Examine whether the given points  A (0,0) and B (5,0) and C (0,6) forms a right triangle.

(6)  Examine whether the given points  P (4,4) and Q (3,5) and R (-1,-1) forms a right triangle.

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