Answer
a) $\left( -1,1 \right)$
b) $\left( 0,13 \right)$
Work Step by Step
(a)
For the point $A=\left( 2,5 \right)$, the $x-$coordinate is $2$, and $y-$coordinate is $5$.
The point $A$ is shifted $3$ units to the left, which means the $x-$coordinate moves horizontally by $3$ units, and it affects only on the $x$-value.
Therefore, to find the new coordinate of the point, subtract (since the shift is to the left) $3$units from the $x-$co-ordinate of the point $\left( 2,5 \right)$.
$\Rightarrow \left( 2-3,5 \right)=(-1, 5)$
Thus, the new ordered pair of the point $A$ is $\left( -1,5 \right)$.
The point $\left( -1,5 \right)$is moved $4$ units down (subtract), which means the shift is vertical, so it affects only on the $y$-value.
Therefore, to find the new coordinate of the point, subtract $4$ units from the $y-$coordinate of the point $\left( -1,5 \right)$.
$\Rightarrow \left(-1,5-4 \right)=(-1, 1)$.
Thus, the ordered pair of the new point $\left( -1,1 \right)$
(b)
For the point $A=\left( 2,5 \right)$, the $x-$coordinate is $2$, and $y-$coordinate is $5$.
The point $A$ is shifted $2$ units to the left, which means the $x-$coordinate moves horizontally by $2$ units, and it affects only the $x-$value.
Therefore, to find the new coordinate of the point, subtract (since the shift is to the left) $2$ units from the $x-$coordinate of the point $\left( 2,5 \right)$.
$\Rightarrow \left( 2-2,5 \right)=(0, 5)$
Thus, the new ordered pair of the point is $\left( 0,5 \right)$.
The point $\left( 0,5 \right)$is moved $8$ units up (add), which means the shift is vertical, so it affects only the $y-$value.
Therefore, the new coordinate of the point can be found, by adding $8$ units to the $y-$coordinate of the point $\left( 0, 5 \right)$.
$\Rightarrow \left( 0, 5+8 \right)=(0, 13)$.
Thus, the new point is $\left( 0,13 \right)$.
