Question

Triangle FGH is translated using the rule (x,y) > (x+3,y-1). What are the coordinates of H ?

Answer 1

Answer: $H'(4,-3)$

Step-by-step explanation:

For this exercise you must remember that the original figure (before a transformation) is called "Pre-Image" and the one obtained after the transformation is called "Image".

 A Translation is defined as a transformation in which the figure is moved a  fixed distance in a fixed direction. In this kind of transformatiosn the size and shape do not change and the figure is not flipped.

In this case you know that the Pre-Image is the Triangle FGH.

You can identify in the picture that its vertex H has these coordinates:

$H(1,-2)$

Where:

$x=1\\y=-2$

Since the rule is:

$(x,y)$ → $(x+3,y-1)$

You can substitute the coordinates of H into the given rule in order to find the coordinates of H'. This is:

$H'=(1+3,-2-1)=(4,-3)$