Find x if distance between points L(x, 7) and M(1, 15) is 10.
Answer:-
L(x, 7), M(1, 15), and LM = 10.
By distance formula,
By distance formula,
\[∴ LM = \sqrt{((x − 1)^2 + (7 − 15)^2)}\]`
\[∴ 10 = \sqrt{((x - 1)^2 + (− 8)^2)}\]
Squaring both the sides, we get,
∴ 100 = (x − 1)2 + 64
∴ 100 = x2 − 2x + 1 + 64
∴ 100 = x2 − 2x + 65
∴ x2 − 2x + 65 − 100 = 0
∴ x2 − 2x − 35 = 0
∴ x2 − 7x + 5x - 35 = 0
∴ x(x − 7) + 5(x − 7) = 0
∴ (x − 7)(x + 5) = 0
∴ x − 7 = 0 or x + 5 = 0
∴ x = 7 or x = −5
x = 7 or x = −5
Chapter 5. Co-ordinate Geometry – Practice Set 5.1 (Page 107)