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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

2. Bisectors of Triangles

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Exercise 52 Page 318

Recall the Midpoint and the Distance Formulas.

Midpoint: (0,5)
AB = 6 units

Practice makes perfect

Let's find the coordinates of the midpoint and the distance one at a time.

Finding the Midpoint

To find the midpoint M, we can use the Midpoint Formula. M(x_1+x_2/2,y_1+y_2/2)The coordinates of the given endpoints are (-3,5) and (3,5). Let's use these to find the coordinates of the midpoint.

M(x_1+x_2/2,y_1+y_2/2)

SubstitutePoints

Substitute ( -3,5) & ( 3,5)

M(-3+ 3/2,5+ 5/2)

Add terms

M(0/2,10/2)

Calculate quotient

M(0,5)

The midpoint is located at (0,5).

Note that the given segment is horizontal. This fact will help us find the distance AB.

Finding the Distance

The given segment is horizontal. Therefore, its length is the difference between the x-coordinates of the endpoints.

We can see that the x-coordinates of the endpoints differ by 6 units. Therefore, AB=6.

Subchapter links

Communicate Your Answer p.309

Monitoring Progress p.311-314

Exercises p.315-318