Question

Find all y such that the distance between the points (-6, -9) and (-4, y) is 28.

Answer 1

Label your points (x1, y1) and (x2, y2). The distance between two points is \[d = \sqrt{\left( x_2-x_1 \right)^2 + (y_2-y_1)^2}\]

Answer 2

\(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -6}}\quad ,&{\color{blue}{ -9}})\quad
% (c,d)
&({\color{red}{ -4}}\quad ,&{\color{blue}{ y_2}})
\end{array}\qquad
% distance value
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}
\\ \quad \\
28 = \sqrt{({\color{red}{ -4}}-{\color{red}{(-6) }})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ (-9)}})^2}\impliedby solve\ for\ {\color{blue}{ y_2}}\)

Answer 3

@jdoe0001 i got -57