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)
$(x_1,y_1)$ $(x_2,y_2)$

Explanation:

Step1: Substitute known values into distance formula

Let $(x_1,y_1)=(-4,-5)$ and $(x_2,y_2)=(x,7)$ and $d = 15$. Then $15=\sqrt{(x - (-4))^2+(7-(-5))^2}$.

Step2: Simplify the equation

First, simplify the right - hand side. $7-(-5)=12$, so the equation becomes $15=\sqrt{(x + 4)^2+12^2}=\sqrt{(x + 4)^2+144}$.

Step3: Square both sides

Squaring both sides gives $15^2=(x + 4)^2+144$. So, $225=(x + 4)^2+144$.

Step4: Isolate the squared term

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

Step5: Solve for x

Take the square root of both sides: $x + 4=\pm\sqrt{81}=\pm9$.
Case 1: If $x + 4=9$, then $x=9 - 4=5$.
Case 2: If $x + 4=-9$, then $x=-9 - 4=-13$.

Answer:

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