Question

Given (9,4) and (x,−11), find all x such that the distance between these two points is 17. Separate multiple answers with a comma.

Answer 1

Answer:

The points are (1, -11) and (17, -11).

Step-by-step explanation:

The distance between points (x1, y1) and (x2, y2) is

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

We have values for x1, y1, and y2. We leave x for x2, and we solve for x.

$17 = \sqrt{(x - 9)^2 + (-11 - 4)^2}$

Square both sides.

$289 = (x - 9)^2 + (-11 - 4)^2$

$289 = x^2 - 18x + 81 + 225$

$x^2 - 18x + 17 = 0$

$(x - 1)(x - 17) = 0 [/tex}[tex] x - 1 = 0$   or   $x - 17 = 0$

x = 1 or x = 17

The points are (1, -11) and (17, -11).