Question

Suppose that A = (3, 4) are the coordinates of a point in the xy-plane. a) Find the coordinates of the point if A is shifted units to the right and down. b) Find the coordinates of the point if A is shifted to the left and units up.

Answer 1

a) (4,3)

b) (2,5)

Point A is at (3, 4):

First, we need to find the coordinates of point A if it shifted a unit to the right and then down.

Shifting either left or right means that there is a change in the x-coordinate of a point. Shifting to the right means we will add while shifting to the left means we will subtract from the x-coordinate.

Shifting upward or downward means there is a change in the y-coordinate. Shifting upwards means we add while shifting downwards means we subtract from the y-coordinate.

Now going back, we have a point A (3, 4)

We are asked to shift a unit to the right, then down. This would mean that we need to add one to the x-coordinate, then subtract 1 from the y-coordinate:

`\begin{gathered} A=(3,4) \\ a=(3+1,4-1) \\ a=(4,3) \end{gathered}`

Representing it with a graph:

Now, we will find the coordinates of point A if it shifted a unit to the left and then up. This would mean that we will subtract from the x-coordinate then add 1 to the y-coordinate:

`\begin{gathered} A=(3,4) \\ b=(3-1,4+1) \\ b=(2,5) \end{gathered}`

Representing it with a graph: