**Vertices of right triangle6 :**

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 6 :**

Examine whether the given points P (4,4) and Q (3,5) and R (-1,-1) 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 P (4,4) and Q (3,5) and R (-1,-1)

Distance between the points P and Q

= **√(x₂ - x₁)² + (y₂ - y₁)²**

Here **x₁ = 4, y₁ = 4, x₂ = 3 and y₂ = 5**

**= **
√(3-4)² + (5-4)²

= ** **
√(-1)² + (1)²

= ** **
√1 + 1

= √2 units

Distance between the points Q and R

= **√(x₂ - x₁)² + (y₂ - y₁)²**

Here **x₁ = 3, y₁ = 5, x₂ = -1 and y₂ = -1**

**= **
√(-1-3)² + (-1-5)²

= ** **
√(-4)² + (-6)²

= ** **
√16 + 36

= √52 units

Distance between the points R and P

= **√(x₂ - x₁)² + (y₂ - y₁)²**

Here **x₁ = -1, y₁ = -1, x₂ = 4 and y₂ = 4**

**= **
√(4-(-1))² + (4-(-1))²

= ** **
√(4+1)² + (4+1)²

= ** **
√5² + (5)²

= √25 + 25

= √50 units

PQ = √2 units

QR = √52 units

RP = √50 units

(QR)² = (PQ)² + (RP)²

(√52)² = (√2)² + (√50)²

52 = 2 + 50

52 = 52

Hence, the given points P,Q and R 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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