Question

Find all y such that the distance between the points (- 9, 3) and (- 2, y) is 8.

Answer 1

We have the following points:

`\begin{gathered} (x_1,y_1)=(-9,3), \\ (x_2,y_2)=(-2,y)\text{.} \end{gathered}`

We must find the values of y such that the distance between the points is d = 8.

The distance between two points (x1, y1) and (x2, y2) is given by:

`d=\sqrt[]{(x_2-x_1)^2+\mleft(y_2-y_1\mright)^2}\text{.}`

Replacing the data of the problem in the equation above, we have:

`\begin{gathered} 8=\sqrt[]{(-2+9)^2+(y-3)^2}, \\ 8=\sqrt[]{49+(y-3)^2}\text{.} \end{gathered}`

Solving the last equation for y, we get:

`\begin{gathered} 8^2=49+(y-3)^2, \\ 64-49=(y-3)^2, \\ (y-3)^2=15. \end{gathered}`

Taking the square root on both sides, we have:

`\begin{gathered} y-3=\pm\sqrt[]{15}, \\ y=3\pm\sqrt[]{15}\text{.} \end{gathered}`

Rounding to one decimal place, we get:

`y\cong6.9\text{ and }y\cong-0.9.`

Rounding to two decimal places, we get:

`y\cong6.87\text{ and }y\cong-0.87.`

Answer

• Rounding to one decimal place: ,6,9,-0.9

,

• Rounding to two decimal places: ,6.87,-0.87