Question

Find x if distance between points L(x, 7) and M(1, 15) is 10. 

Answer 1

L(x, 7), M(1, 15), and LM = 10.

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

∴ (x − 1)² = 100 − 64

∴ (x − 1)² = 36

Taking square roots of both the sides,

∴ x − 1 = `+-` 6

∴ x − 1 = 6        or        x - 1 = −6

∴ x = 6 + 1       or        x = −6 + 1

∴ x = 7       or        x = −5

x = 7 or x = −5

Answer 2

L(x, 7), M(1, 15), and LM = 10.

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