Q36. - Precalculus Enhanced with Graphing Utilities

Question

Find two numbers $y$ such that the distance from$\left(-3,2\right)$ to $\left(5,y\right)$ is $10$.

Step-by-Step Solution

Answer

Two numbers of $y$ are $8$ and $-4$.

Step 1. Given information.

Consider the given information such that the points are $\left(-3,2\right)$ and $\left(5,y\right)$.

Step 2. Formula used

The formula for finding distance between two points is given by $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Step 3. Using distance formula to calculate the value of y .

Substitute values of $x_1=-3, x_2=5$ and $y_1=2,y_2=y$ into the distance formula.

$$\begin{gathered} 10=\sqrt{{\left(5+3\right)}^2+{\left(y-2\right)}^2} \\ 10=\sqrt{64+{\left(y-2\right)}^2} \\ 100=64+{\left(y-2\right)}^2 \end{gathered}$$

Futher simplify

$$\begin{gathered} 36={\left(y-2\right)}^2 \\ {y}^2-4y-32=0 \\ y=8, y=-4 \end{gathered}$$