Question

Find the values of x for which the distance between the point P(2, -3) and Q(x, 5) is 10 units.

Answer 1

Answer: x = 8, -4

Step-by-step explanation:

Distance formula = $\sqrt{ (x2 - x1)^{2} + (y2 - y1)^{2} }$

Where x1,y1 and x2,y2 are the coordinates of the points

Using this formula, we get

$\sqrt{ (x-2)^{2} + (t+3)^{2} } = 10$

Squaring on both sides, we get

$(X-2)^{2} + 8^{2} = 100\\\\=> x^{2} + 4 - 4x + 64 = 100\\\\=> x^{2} - 4x = 32\\\\=> x^{2} - 4x -32 = 0\\\\=> x^{2} - 8x + 4x - 32 = 0\\\\=> (x-8)*(x+4) = 0\\\\=> x = 8, -4$

Therefore the coordinates are 8 or -4

Please brainlist my answer, if helpful!