Question

Given A(-2. 0), B(6,3) and C(0,8)

What is the rule for translating up 4 units and left 2 units?

Answer 1

The rule for translating up 4 units and left 2 units is to substract 2 from all the "x" values and add 4 to all the "y" values.

This is the result after applying the rule for all 3 points:

`A(-4, 4)\\\\B(4,7)\\\\C(-2,12)`

Explanation:

Let's solve step by step.

Moving the points left 2 units.

Remember that on ordered pairs, the horizontal position is defined by the x axis, and the x axis is always the first number on the ordered pair. For example, point A(-2. 0) is located 2 units to the left of the y axis. Therefore, to move it 2 places to the left from its current position, we substract 2 units from the current x value. This is what we are doing:

`A( (-2-2) , 0) = A(-4, 0)`

Do the same for all points:

`B((6-2),3)=B(4,3)\\\\C((0-2),8)=C(-2,8)`

Moving the points up 4 units.

In order to change the position vertically, we do the same we did previously, except this time we are going to be working with the second value inside each parenthesis. To move up the point, we add up 4 to its value. Do it in the following fashion:

`A(-4, (0+4))=A(-4, 4)\\\\B(4,(3+4))=B(4,7)\\\\C(-2,(8+4))=C(-2,12)`

Final answer.

The rule for translating up 4 units and left 2 units is to substract 2 from all the "x" values and add 4 to all the "y values.