Question 84774
 Find the possible values of y if the points (-7,-9) and (-10, y) are a distance d=squareroot 178 apart. Hod do I do this?
:
Remember the distance formula:
d = {{{sqrt((x2-x1)^2 + (y2-y1)^2)}}}; In this problem: x1 = -7, x2 = -10; y1 = -9; y2 = y
:
Substitute for x1, x2, y1, y2, and d
{{{sqrt((-10-(-7))^2 + (y-(-9))^2)}}} = {{{sqrt(178)}}}
:
{{{sqrt((-10+7)^2 + (y+9))^2)}}} = {{{sqrt(178)}}}
:
Squaring both sides gets rid of the radicals:
{{{(-10+7)^2 + (y+9)^2}}} = 178
:
{{{-3^2 + (y^2 + 18y + 81)}}} = 178
:
y^2 + 18y + 81 + 9 - 178 = 0
:
y^2 + 18y - 88 = 0
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Factors to:
(y + 22)(y - 4) = 0
:
y = +4 and y = -22
:
:
you can check both solutions in the distance equation;
They should = {{{sqrt(178)}}}