Question

Point B has coordinates (5, 1) The x coordinate of point A is 0 . The distance between point A and Point B is 13 units. What are the possible coordinates of point A?

Answer 1

Let y represent the y-coordinate of point A.

We have been given that point B has coordinates (5,1) The x-coordinate of point A is 0. So coordinates of point A would be (0,y)

The distance between point A and Point B is 13 units.

We will use distance formula to solve our given problem.

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

Let point A
`(0,y)=(x_2-y_2)` and point A
`(5,1)=(x_1,y_1)`.

Upon substituting coordinates of both points in distance formula, we will get:

`13=√((0-5)^2+(y-1)^2)`

`13=√(25+y^2-2y+1)`

`13=√(y^2-2y+26)`

Let us square both sides as:

`13^2=(√(y^2-2y+26))^2`

`169=y^2-2y+26`

`169-169=y^2-2y+26-169`

`0=y^2-2y-143`

`y^2-2y-143=0`

Upon splitting the middle term, we will get:

`y^2-13y+11y-143=0`

`y(y-13)+11(y-13)=0`

`(y-13)(y+11)=0`

Now we will use zero product property.

`(y-13)=0, (y+11)=0`

`y=13, y=-11`

Therefore, the possible coordinates of point A would be
`(0,-11)` and
`(0,13)`.