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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

1. Translations

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Exercise 42 Page 552

Line perpendicular to a vertical line is horizontal.

y = - 2

Practice makes perfect

To write the equation of a line perpendicular to the one whose equation is given, we first need to determine its slope.

The Perpendicular Line's Slope

Notice that we are given a vertical line. x = - 2

We know that a line perpendicular to a vertical line is always horizontal. The slope of any horizontal line is equal to 0.

Writing the Perpendicular Line's Equation

Using the slope 0, we can write a general equation in slope-intercept form for all lines perpendicular to the given equation. y= x + b By substituting the given point ( 1, - 2) into this equation for x and y, we can solve for the y-intercept b of the perpendicular line.

y = 0x + b

x= 1, y= - 2

- 2=0( 1)+b

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Solve for b

Multiply

- 2 = 0 + b

Identity Property of Addition

- 2 = b

Rearrange equation

b=- 2

Now that we have the y-intercept, we can complete the equation. The line given by this equation is both perpendicular to x=- 2 and passes through the point (1,- 2). y= 0x+(- 2) ⇔ y = - 2

Subchapter links

Lesson Check p.549

Standardized Test Prep p.552

Mixed Review p.552