**Vertices of right triangle1 :**

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

**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.

**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.

(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.

- Solution of vertices of right triangle question 1
- Solution of vertices of right triangle question 2
- Solution of vertices of right triangle question 3
- Solution of vertices of right triangle question 4
- Solution of vertices of right triangle question 5
- Solution of vertices of right triangle question 6

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