Find the value of

Given;

PA = PB

P (2, 4)

A (5, k)

B (k, 7)

By squaring both sides;

PA² = PB²

(5 – 2)² + (k – 4)² = (k – 2)² + (7 – 4)²

9 + (k – 4)² = (k – 2)² + 9

9 + (k – 4)² – (k – 2)² = 9

(k – 4)² – (k – 2)² = 9 – 9

(k – 4)² – (k – 2)² = 0

[k² – (4)² + 8k]- [k² – (2)² + 4k] = 0 ……{by (a-b)² = a² – b² + 2ab}

k² – 16 + 8k – k² + 4 – 4k = 0

- 12 + 4k = 0

4k = 12

k = 12/4 = 3

Therefore the value of k is 3.