Question

Point A(9,-6) is translated using the rule (x+3, y-7) then it is reflected across the x-axis. What are the coordinates of its final image?

Answer 1

The coordinates of its final image are
`(x'', y'') = (12, 13)`.

Explanation:

From Linear Algebra, we define reflection across the x-axis as:

`(x',y') = (x, -y)`,
`\forall \,x,y\in\mathbb{R}`

According to the statement of problem, the following operation of translation:

`(x',y') = (x+3, y-7)`,
`\forall \,x,y\in \mathbb{R}`

Where:

`(x,y)` - Original point, dimensionless.

`(x',y')` - Translated point, dimensionless.

If we know that
`A(x, y) = (9, -6)`, we proceed to make the abovementioned operations:

Translation

`(x', y') = (9+3,-6-7)`

`(x',y') = (12, -13)`

Reflection

`(x'', y'') = (x',-y')`

`(x'', y'') = (12, 13)`

The coordinates of its final image are
`(x'', y'') = (12, 13)`.