Question

A rectangle on a coordinate plane is translated $5$ units up and $3$ units to the left.

Which rule describes the translation?

• A. $\left(x,y\right)\to \left(x+5,y-3\right)$
• B. $\left(x,y\right)\to \left(x+5,y+3\right)$
• C. $\left(x,y\right)\to \left(x-3,y+5\right)$
• D. $\left(x,y\right)\to \left(x+3,y+5\right)$

Answer 1

The correct option is C

$\left(x,y\right)\to \left(x-3,y+5\right)$

Finding the correct option.

The rectangle is translated $5$ units up and $3$ units to the left.

In a rectangular coordinate system, when the translation is done upwards or downwards, then the $y-$coordinate changes. It becomes positive during upward translation and negative during downward translation. Since the rectangle is translated $5$ units up, the modified $y-$ coordinate will be $y+5$.

Similarly, when the left or right translation is made, then $x-$ coordinate changes. For left translation, the $x-$ coordinate becomes negative and for right translation, the $x-$coordinate becomes positive. Since the rectangle is translated $3$ units to the left, the modified $x-$coordinate will be $x-3$.

Therefore, after both the translations, $\left(x,y\right)\to \left(x-3,y+5\right)$.

Hence, $\mathbf{\left(}\mathit{C}\mathbf{\right)}$ is the correct option.