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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Cumulative Standards Review

Exercise 19 Page 820

Calculate the slopes of the lines using the Slope Formula.

Slope of HK: - 23
Slope of MN: 32
Relationship Between the Line Segments: Perpendicular

Practice makes perfect

Let's calculate each of the slopes separately and then identify the relationship between the line segments.

Slope of HK

We are given the endpoints H(-3,7) and K(6,1) of the segment line HK. Let's substitute them into the Slope Formula and calculate the slope.

m_1=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -3,7) & ( 6,1)

m_1=1- 7/6-( -3)

▼

Simplify

a-(- b)=a+b

m_1=1-7/6+3

Add and subtract terms

m_1=-6/9

a/b=.a /3./.b /3.

m_1=-2/3

MoveNegNumToFrac

Put minus sign in front of fraction

m_1=- 2/3

Slope of MN

Similarly, by substituting the endpoints M(-5,-8) and N(7,10) into the Slope Formula, we can calculate the slope of the line segment MN.

m_2=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -5,-8) & ( 7,10)

m_2=10-( -8)/7-( -5)

a-(- b)=a+b

m_2=18/12

a/b=.a /6./.b /6.

m_2=3/2

Analyze the Slopes

Now that we know the slopes of the lines, we can determine whether they are parallel, perpendicular, or neither. Remember that parallel slopes are the same and perpendicular slopes are opposite reciprocals. m_1=- 2/3 m_2=3/2 These slopes are opposite reciprocals, so the lines are perpendicular. Let's graph the lines to verify that they are perpendicular. We do can this by plotting the points and drawing segments connecting them.

As we can see, the segment lines are truly perpendicular.