The distance between the points (-3, 2) and (x, 10) is 10 units. The value of x is :

1. 3

2. -9

3. 3 or -9

4. 3 and -9

Let (-3, 2) = (x₁, y₁) and (x, 10) = (x₂, y₂)

Distance between the given points =

$\sqrt{(x$2 - x1)^2 + (y2 - y1)^2}\\[1em] 10 = \sqrt{(x - (-3))^2 + (10 - 2)^2}\\[1em] ⇒ 10 = \sqrt{(x + 3)^2 + 8^2}\\[1em] ⇒ 10^2 = (x + 3)^2 + (8)^2\\[1em] ⇒ 100 = (x + 3)^2 + 64\\[1em] ⇒ 100 - 64 = (x + 3)^2\\[1em] ⇒ 36 = (3 + x)^2\\[1em] ⇒ \sqrt{36} = 3 + x\\[1em] ± 6 = 3 + x\\[1em] 6 = x + 3 \text{ or} -6 = 3 + x \\[1em] x = 6 - 3 \text{ or} -6 -3 = x \\[1em] x = 3 \text{ or} -9\\[1em]

Hence, option 3 is the correct option.