  ### Home > INT2 > Chapter 12 > Lesson 12.2.4 > Problem12-140

12-140.

Graph and connect the points $G(-2, 2),$ $H(3, 2),$ $I(6, 6),$ and $J(1, 6)$ to form $GHIJ$.

1. What specific type of shape is quadrilateral $GHIJ$? Justify your conclusion

Use the Pythagorean Theorem and the triangles shown to determine the lengths of $GJ$ and $HI$.

What type of quadrilateral (other than a square) has sides all of the same length?

2. Write the equations of the diagonals $GI$ and $HJ$.

Use slope triangles to find the equations for the diagonals.

3. Compare the slopes of the diagonals. How do the diagonals of a rhombus appear to be related?

If one line has a slope that is the opposite of the reciprocal of the slope of another line, the two lines are perpendicular.

4. Determine the coordinates of point $J'$ if quadrilateral $GHIJ$ is rotated $90°$ clockwise $(\circlearrowright)$ about the origin.

1. Calculate the area of quadrilateral $GHIJ$.

Area of a parallelogram $= (b)(h)$.

Move the points in the eTool to their given coordinates. The shape will appear when all the points are in their proper places.
Click the link at right for the full eTool version: 12-140 HW eTool (Desmos)