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

Answer:

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

Step-by-step 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 $(x'', y'') = (12, 13)$.