Question

practice: find the possible values for the missing coordinate given: d = 15
$d=sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ (-4,-5) & (x,7)
$(x_1,y_1)$ $(x_2,y_2)$
$15=sqrt{(x - - 4)^2+(7 - - 5)^2}$
$15=sqrt{(x - - 4)^2+144}$

Explanation:

Step1: Square both sides of the equation

Given $15=\sqrt{(x - (-4))^{2}+144}$, squaring both sides gives $15^{2}=(x + 4)^{2}+144$. So, $225=(x + 4)^{2}+144$.

Step2: Isolate the squared - term

Subtract 144 from both sides: $(x + 4)^{2}=225 - 144$. Then $(x + 4)^{2}=81$.

Step3: Take the square root of both sides

We have $x + 4=\pm\sqrt{81}$. So $x + 4=\pm9$.

Step4: Solve for x

Case 1: When $x + 4 = 9$, then $x=9 - 4=5$.
Case 2: When $x + 4=-9$, then $x=-9 - 4=-13$.

Answer:

$x = 5$ or $x=-13$