Question

The distance between the points $P(2, -3)$ and $Q(10, v)$ is 10 units. The value of $v$ will be:

• A. $-3, 9$
• B. $-9, 3$
• C. $9, 3$
• D. $-9, 2$

Hint:

Use the distance formula to find the distance between two points. For points $(x_1, y_1)$ and $(x_2, y_2)$, the formula is: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Answer 1

The Correct Option is C

The distance between two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ is given by the formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] For the points $P(2, -3)$ and $Q(10, v)$, the distance is given as 10 units: \[ 10 = \sqrt{(10 - 2)^2 + (v - (-3))^2} \] \[ 10 = \sqrt{8^2 + (v + 3)^2} \] \[ 10 = \sqrt{64 + (v + 3)^2} \] \[ 100 = 64 + (v + 3)^2 \] \[ (v + 3)^2 = 36 \] \[ v + 3 = \pm 6 \] So, \[ v = 6 - 3 = 3 \quad \text{or} \quad v = -6 - 3 = -9 \] Thus, the values of $v$ are $9$ and $3$.