Question

Find k so that the distance from (–1, 1) to (2, k) is 5 units.

Answer 1

Answer:

k = -3 or 5

Step-by-step explanation:

The given parameters are;

The line extends from points (-1, 1) to point (2, k)

The length of the line = 5 units

The formula for the length, l, of a line given its coordinates can be  found by the following formula;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

Therefore, we have;

$5 = \sqrt{\left (k-1 \right )^{2}+\left (2-(-1) \right )^{2}}$

Which, by squaring both sides, gives;

25 = (k - 1)² + (2 - (-1))² = (k - 1)² + (2 + 1)² = (k - 1)² + 3²

25 = (k - 1)² + 3² = k² - 2·k + 1 + 9

25 - 25 = 0 = k² - 2·k + 1 + 9 - 25 = k² - 2·k - 15

0 = k² - 2·k - 15

0 = (k +3) × (k - 5)

Therefore, k = -3 or 5

When k - -3, we have;

$\sqrt{\left ((-3)-1 \right )^{2}+\left (2-(-1) \right )^{2}}= \sqrt{(-4)^2+3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$

When k = 5, we have;

$\sqrt{\left (5-1 \right )^{2}+\left (2-(-1) \right )^{2}}= \sqrt{4^2+3^2} = 5$