body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Rectangles

Continue to next subchapter

Exercise 22 Page 509

A rectangle is a parallelogram with four right angles.

Graph:

Is It a Rectangle? Yes, see solution.

Practice makes perfect

Let's plot the given points and draw the quadrilateral on a coordinate plane.

We can use the Slope Formula to determine whether the figure is a rectangle. Recall that a rectangle is type of a parallelogram that has four right angles. Let's find the slope of each side.

Side	Slope Formula	Simplify
Slope of WX, ( -2,4), ( 5,5)	5- 4/5-( -2)	1/7
Slope of XY, ( 5,5), ( 6, -2)	-2- 5/6- 5	- 7
Slope of ZY, ( - 1, - 3), ( 6, -2)	-2-( - 3)/6-( - 1)	1/7
Slope of WZ, ( - 2,4), ( -1, -3)	-3- 4/- 1-( - 2)	- 7

The slopes of the opposite sides of our quadrilateral are equal, so both pairs of opposite sides are parallel. Therefore, we know that the quadrilateral is a parallelogram. We can also tell that the consecutive side are perpendicular, as their slopes are opposite reciprocals. 1/7 * (- 7) = -1 Therefore, our quadrilateral is a rectangle, as it has four right angles.

Subchapter links

Exercises p.508-511