Question

Determine another point on the parabola that has an axis of symmetry x = 4 and a point on the parabola is (0, 2), Another point on the parabola is

Answer 1

Given:

Axis of symmetry of a parabola is
`x=4`.

A point on the parabola is (0,2).

To find:

The another point on the parabola.

Solution:

The point (0,2) lies on the parabola and the axis of symmetry of a parabola is
`x=4`.

It means, the another point on the parabola is the mirror image of (0,2) across the line
`x=4` because the parabola is symmetric about the axis of symmetry.

If the point is reflected across the line
`x=4`, then

`(x,y)\to (-(x-4)+4,y)`

`(x,y)\to (-x+4+4,y)`

`(x,y)\to (-x+8,y)`

Using this rule, we get

`(0,2)\to (-0+8,2)`

`(0,2)\to (8,2)`

Therefore, the other point on the parabola is (8,2).