Chapter 1.1, Problem 49AYU

Suppose that $A=\left(2,5\right)$ are the coordinates of a point in the $xy$-plane.

Find the coordinates of the point if $A$ is shifted $3$ units to the left and $4$ units down.

Find the coordinates of the point if $A$ is shifted $2$ units to the left and $8$ units up.

To determine

The new co-ordinates of the point $A=\left(2,5\right)$, if the point $A$ is shifted 3 units to the left and 4 units down.

Answer to Problem 49AYU

Solution:

The new co-ordinates of the point $A=\left(2,5\right)$, if the point $A$ shifted 3 units to the left and 4 units down, is $\left(-1,1\right)$.

Explanation of Solution

Given Information:

The point $A=\left(2,5\right)$ is shifted 3 units to the left and 4 units down.

Explanation:

For the point $A=\left(2,5\right)$, $x-$ co-ordinate is 2, and $y-$ coordinate is 5.

The point $A$ is shifted 3 units to the left, which means the $x-$ co-ordinate moves horizontally by 3 units, and it affects only on $x$ values.

Therefore, to find the new coordinate of the point, subtract (since shift left) 3 units from the $x-$ co-ordinate of the point $\left(2,5\right)$.

$\Rightarrow \left(2-3,5\right)$

Thus, the new ordered pair of the point $A$ is $\left(2-3,5\right)$.

The point $\left(2-3,5\right)$ is moved 4 units down (subtract), which means the shift is vertical, so it affects only on $y$ values.

Therefore, to find the new coordinate of the point, subtract 4 units from the $y-$ co-ordinate of the point $\left(2-3,5\right)$.

$\Rightarrow \left(2-3,5-4\right)$.

Thus, the ordered pair of the new point $\left(-1,1\right)$.

To determine

The new co-ordinates of the point $A=\left(2,5\right)$, if the point $A$ is shifted 2 units to the left and 8 units up.

Answer to Problem 49AYU

Solution:

The new co-ordinates of the point $A=\left(2,5\right)$, if the point $A$ is shifted 2 units to the left and 8 units up, is $\left(0,13\right)$.

Explanation of Solution

Given Information:

The point $A=\left(2,5\right)$ is shifted 2 units to the left and 8 units up.

Explanation:

For the point $A=\left(2,5\right)$, $x-$ co-ordinate is 2, and $y-$ coordinate is 5.

The point $A$ is shifted 2 units to the left, which means the $x-$ co-ordinate moves horizontally by 2 units, and it affects only on $x$ values.

Therefore, to find the new coordinate of the point, subtract (since shift left) 2 units from the $x-$ co-ordinate of the point $\left(2,5\right)$.

$\Rightarrow \left(2-2,5\right)$

Thus, the new ordered pair of the point is $\left(2-2,5\right)$.

The point $\left(2-2,5\right)$ is moved 8 units up (add), which means the shift is vertical, so it affects only on $y$ values.

Therefore, the new coordinate of the point can be found, by adding 8 units to the $y-$ co-ordinate of the point $\left(2-2,5\right)$.

$\Rightarrow \left(2-2,5+8\right)$.

By simplifying,

Thus, the new point is $\left(0,13\right)$.