Chapter 12.4, Problem 3C

To determine

To draw the quadrilateral with the given vertices. To find the coordinates of the vertices of the image after the translation and draw the image.

Answer to Problem 3C

The quadrilateral $\text{JKLM}$ and image $\text{J'K'L'M'}$ can be represented on a graph as:

Explanation of Solution

Given information:

The coordinates of quadrilateral $\text{JKLM}$ provided in the question:

$\text{J(-5,0), K(-2,0), L(3,-4), M(-2,-4)}$

The provided coordinate notation for translation:

$(x,y)\to (x+7,y+4)$

As per the problem

Consider the vertices of the quadrilateral $\text{JKLM}$ :

  $\text{J(-5,0), K(-2,0), L(3,-4), M(-2,-4)}$

The quadrilateral $\text{JKLM}$ can be drawn as follows:

To translate quadrilateral $\text{JKLM}$ , consider the coordinate notation:

  $(x,y)\to (x+7,y+4)$

Add $7$ to the $x$ coordinate and $4$ to the $y$ coordinate of each vertex

Original Image

$(x,y)\to (x+7,y+4)$

$\text{J(-5,0)}\to \text{J'(2,4)}$

$\text{ K(-2,0)}\to \text{K'(5,4)}$

  $\text{ L(3,-4)}\to \text{L'(10,0)}$

  $\text{ M(-2,-4)}\to \text{M'(5,0)}$

The image $\text{J'K'L'M'}$ using the above coordinates will be as follows:

Conclusion: The image $\text{J'K'L'M'}$ has moved $7$ unit to the right and $4$ units up from the original quadrilateral $\text{JKLM}$ .