# If Q(0, 1) is equidistant from P(5, - 3) and R (x, 6), find the values of x. Also, find the distances QR and PR

**Solution:**

We know that the distance between the two points is given by the Distance Formula = √[( x_{2 - }x_{1 })^{2} + (y_{2} - y_{1})^{2}]

Q (0, 1) is equidistant from P (5, - 3) and R (x, 6), so, PQ = QR

Hence by applying the distance formula for the PQ = QR, we get

√(5 - 0)² + (-3 - 1)² = √(0 - x)² + (1 - 6)²

√(5)² + (- 4)² = √(- x)² + (- 5)²

By squaring both the sides,

25 + 16 = x^{2} + 25

16 = x^{2}

x = ± 4

Therefore, point R is (4, 6) or (- 4, 6).

Case (1): When point R is (4, 6),

Distance between P (5, - 3) and R (4, 6) can be calculated using the Distance Formula as,

PR = √(5 - 4)² + (- 3 - 6)²

= √1² + (- 9)²

= √1 + 81

= √82

Distance between Q (0, 1) and R (4, 6) can be calculated using the distance formula as,

QR = √(0 - 4)² + (1 - 6)²

= √(- 4)² + (- 5)²

= √16 + 25

= √41

Case (2): When point R is (- 4, 6)

Distance between P (5, - 3) and R (- 4, 6) can be calculated using the distance formula as,

PR = √(5 - (- 4))² + (- 3 - 6)²

= √(9)² + (- 9)²

= √81 + 81

= 9√2

Distance between Q (0, 1) and R (- 4, 6) can be calculated using the distance formula as ,

QR = √(0 - (- 4))² + (1 - 6)²

= √(4)² + (- 5)²

= √16 + 25

= √41

**Video Solution:**

## If Q (0, 1) is equidistant from P (5, - 3) and R (x, 6), find the values of x. Also, find the distances QR and PR

### NCERT Class 10 Maths Solutions - Chapter 7 Exercise 7.1 Question 9:

If Q (0, 1) is equidistant from P (5, - 3) and R (x, 6), find the values of x. Also, find the distances QR and PR

Final Answer: The value of x for which Q (0, 1) is equidistant from P (5, - 3) and R (x, 6) is 4, - 4