Question

Point b has coordinates (1,2). The x-coordinate of point a is -2. The distance of point a and point b is 5 units. What are the possible coordinates of point a?

Answer 1

`(-2,6)` and
`(-2,-2)`.

Explanation:

We have been given that point b has coordinates (1,2). The x-coordinate of point a is -2. The distance of point a and point b is 5 units.

We will use distance formula to solve our given problem.

`D=√((x_2-x_1)+(y_2-y_1)^2)`

Let us assume that (1,2) is
`(x_1,y_1)` and point
`(-2,y)=(x_2,y_2)`

`5=√((-2-1)^2+(y-2)^2)`

`5=√((-3)^2+(y-2)^2)`

`5=√(9+y^2-4y+4)`

`5=√(y^2-4y+13)`

Square both sides:

`5^2=(√(y^2-4y+13))^2`

`25=y^2-4y+13`

`y^2-4y+13-25=0`

`y^2-4y-12=0`

`y^2-6y+2y-12=0`

`(y-6)(y+2)=0`

`(y-6)=0,(y+2)=0`

`(y=6,y=-2`

Therefore, the possible coordinates of point 'a' are
`(-2,6)` and
`(-2,-2)`.