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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Chapter Review

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Exercise 9 Page 408

Start by plotting the given vertices and drawing two sides.

M(2,-2)

Practice makes perfect

To find the coordinates of the missing vertex M, we will follow four steps.

Plot the given vertices and draw two sides of the parallelogram.
Find the slope of one of the sides.
Use the rise and run of the obtained slope to find the missing vertex.
Verify that the sides are parallel.

Let's do it!

Plotting the Vertices

We know that three of the vertices are J(1,4), K(5,3), and L(6,- 3). Let's plot them on a coordinate plane and draw two of the sides of the parallelogram.

Finding the Slope of BA

Using our graph, we will find the slope of KJ.

Using the observed changes in x and y, we can write the slope of KJ. Slope=Rise/Run ⇔ Slope= 1/- 4=- 1/4

Finding the Missing Vertex

By definition, opposite sides of a parallelogram are parallel. Therefore, the slope of LM will be the same as the slope of KJ. Let's start at L and use the rise and run from the previous step to find vertex M.

The missing vertex M occurs at the point (2,-2). Let's draw the parallelogram.

Verifying that the Sides are Parallel

By construction, we already know that KJ ∥ LM. However, for us to be certain that our quadrilateral is a parallelogram, we need both pairs of opposite sides to have equal slopes. Let's calculate the slopes of MJ and LK, and check that they are the same.

The slopes of DA and CB are equal! Slope=Rise/Run ⇔ Slope= 6/-1 =-6 Therefore, the opposite sides are parallel and the polygon is a parallelogram.

Subchapter links

Exercises p.408-410