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McGraw Hill Glencoe Geometry, 2012

MH

McGraw Hill Glencoe Geometry, 2012 View details

6. Perpendiculars and Distance

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Exercise 21 Page 221

Notice that the lines are horizontal. What is the equation of a perpendicular line?

$6$

Practice makes perfect

We are given two horizontal lines.

y = - 2 y = 4

Therefore, the line perpendicular to both lines could be any vertical line. Let's consider the line

x = 1 .

It intersects the lines at

P (1, - 2)

and

Q (1, 4) .

The distance between these two lines is the distance between

P

and

Q .

Let's use the Distance Formula to find it!

d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

SubstitutePoints

Substitute $(1, - 2)$ & $(1, 4)$

d = (1 - 1)^{2} + (4 - (- 2))^{2}

▼

Simplify right-hand side

$a - (- b) = a + b$

d = (1 - 1)^{2} + (4 + 2)^{2}

Add and subtract terms

d = 0^{2} + 6^{2}

Calculate power

d = 0 + 36

Add terms

d = 36

Calculate root

d = 6

Therefore, the distance between the lines is

6

units.

Subchapter links

Check Your Understanding p.220

Practice and Problem Solving p.220-223

H.O.T. Problems p.223

Standardized Test Practice p.224

Spiral Review p.224

Skills Review p.224