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Big Ideas Math Geometry, 2014

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Big Ideas Math Geometry, 2014 View details

5. Equations of Parallel and Perpendicular Lines

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Exercise 24 Page 160

The shortest distance between a point and a line is the length of the line segment that is perpendicular to the given line.

About $1.7$ units

Practice makes perfect

The shortest distance between a point and a line is the length of the line segment that is perpendicular to the given line. We will need to find the perpendicular line and then we can find the intersection point. Finally, we can calculate the distance from the given point to the point of intersection.

Finding the Perpendicular Line

Perpendicular lines have negative reciprocal slopes. This means the product of their slopes is equal to

- 1 .

m_{1} \cdot m_{2} = - 1

To help us identify the slope of the given line, let's first convert it into slope-intercept form.

- x + 2 y = 14

▼

Write in slope-intercept form

$LHS + x = RHS + x$

2 y = x + 14

$LHS / 2 = RHS / 2$

y = \frac{x + 1 4}{2}

Write as a sum of fractions

y = \frac{x}{2} + \frac{1 4}{2}

$\frac{a}{b} = \frac{1}{b} \cdot a$

y = \frac{1}{2} x + \frac{1 4}{2}

Calculate quotient

y = \frac{1}{2} x + 7

Subchapter links

Communicate Your Answer p.155

Monitoring Progress p.156-159

Exercises p.160-162