Question

Point B has coordinates (1,2).The x-coordinate of point A -7 is . The distance between point A and point B is 10 units. What are the possible coordinates of point A?

Answer 1

`The\text{ possible coordinates are \lparen-7,-4\rparen or \lparen-7,8\rparen}`

Step-by-step explanation:

Here, we want to get the possible coordinates of point A

The distance between two points can be calculated as follows:

`D\text{ = }√(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

Let the y-coordinate of A be y

So we have the coordinates to use as (-7,y) and (1,2)

Substituting the values, we have it that:

`10\text{= }√(\left(1+7\right)^2+\left(2-y\right)^2)`

Square both sides:

`\begin{gathered} 10^2\text{ = 8}^2\text{ + \lparen2-y\rparen}^2 \\ 10^2-8^2\text{ = \lparen2-y\rparen}^2 \\ \lparen \end{gathered}`
`\lparen2-y)\placeholder{⬚}^2=\text{ 36}`
`\begin{gathered} 2-y\text{ = + 6 or 2-y = -6} \\ y\text{ = 2-6 or y= 2+6} \\ .y\text{ = -4 or 8} \end{gathered}`

The possible coordinates of A are (-7,-4) or (-7,8)