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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

1. Congruent Figures

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Exercise 54 Page 224

The slopes of perpendicular lines are negative reciprocals.

y=-2/3x+25/3

Practice makes perfect

Consider the given equation of a line. y=3/2x-2 To find the slope perpendicular to this line, we need to find the negative reciprocal of 32.

m_1 * m_2 = -1

m_1= 3/2

3/2 * m_2 = -1

LHS * 2/3=RHS* 2/3

m_2 = - 2/3

We found that - 23 is the negative reciprocal of 32. Because of this, we know that all lines that are perpendicular to the line whose equation is given will have a slope of - 23. We can write a general equation in slope-intercept form for these lines. y=-2/3x+ b We are asked to write the equation of a line parallel to the one with given equation that passes through the point P( 2, 7). By substituting this point into the above equation for x and y, we will be able to solve for the y-intercept b of the perpendicular line.

y=-2/3x+b

x= 2, y= 7

7=-2/3( 2)+b

MoveRightFacToNum

a/c* b = a* b/c

7=-4/3+b

Write as a fraction

21/3=-4/3+b

LHS+4/3=RHS+4/3

25/3=b

Rearrange equation

b=25/3

Now that we have the y-intercept, we can write the perpendicular line to y= 32x-2 passing through P(2,7). y=-2/3x+ 25/3

Subchapter links

Lesson Check p.221

Practice and Problem-Solving Exercises p.222-224

Standardized Test Prep p.224

Mixed Review p.224