## VERTICES OF RIGHT TRIANGLE1

Vertices of right triangle1 :

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

## How to check whether the given points form a right triangle ?

Step 1 :

After naming the given points, we have to find the length of each side of the given triangle using the formula distance between two points.

Step 2 :

We can pythagorean theorem,

That is,

Square of length of larger side  =  sum of the squares of other two sides

Step 3 :

If the given points satisfies the above condition, we can decide that the given points form a right triangle.

## Vertices of right triangle1 - Solution

Question 1 :

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

Solution :

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

√(x₂ - x₁) ² + (y₂ - y₁) ²

The three points are  A (-3,-4) and B (2,6) and C(-6,10)

Distance between the points A and B

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = -3, y₁ = -4, x₂ = 2  and  y₂ = 6

√(2-(-3))² + (6-(-4))²

=   √(2+3)² + (6+4)²

=  √5² + 10²

=   √25 + 100

=   √125 units

Distance between the points B and C

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 2, y₁ = 6, x₂ = -6  and  y₂ = 10

=    √(-6-2)² + (10-6)²

=    √(-8)² + (4)²

=    √64 + 16

=    √80 units

Distance between the points C and A

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = -6, y₁ = 10, x₂ = -3  and  y₂ = -4

=    √(-3-(-6))² + (-4-10)²

=    √(-3+6)² + (-14)²

=    √3² + (-14)²

=    √9 + 196

=    √205 units

AB = √125 units

BC = √80 units

CA = √205 units

(CA)² = (AB)² + (BC)²

(√205)²  = (√125)² + (√80)²

205 = 125 + 80

205 = 205

Hence, the given points forms a right triangle.

## Try other questions

(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. ## Related topics

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