Lesson 11

Perpendicular Lines in the Plane

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Problem 1

Write an equation for a line that passes through the origin and is perpendicular to \(y=5x-2\).

Solution

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Problem 2

Match each line with a perpendicular line. 

A:

\(y=5x+2\)

B:

\(y-2.25=\text-2(x-2)\)

C:

the line through \((\text-1,5)\) and \((1,9)\)

1:

the line through \((2,12)\) and \((17,9)\)

2:

\(y=\text-\frac{1}{2} x+5\)

3:

\(2x-4y=10\)

Solution

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Problem 3

The  rule \((x,y)\rightarrow (y,\text-x)\) takes a line to a perpendicular line. Select all the rules that take a line to a perpendicular line. 

A:

\((x,y)\rightarrow (2y,\text-x)\)

B:

\((x,y)\rightarrow (\text-y,\text-x)\)

C:

\((x,y)\rightarrow(\text-y,x)\)

D:

\((x,y)\rightarrow(0.5y,\text-2x)\)

E:

\((x,y)\rightarrow(4y,\text-4x)\)

Solution

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Problem 4

  1. Write an equation of the line with \(x\)-intercept \((3,0)\) and \(y\)-intercept \((0,\text-4)\).
  2. Write an equation of a line parallel to the line \(y-5=\frac43(x-2)\).

Solution

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(From Unit 6, Lesson 10.)

Problem 5

Lines \(\ell\) and \(p\) are parallel. Select all true statements.

Coordinate plane. Two lines.
A:

Triangle \(ADB\) is similar to triangle \(CEF\).

B:

Triangle \(ADB\) is congruent to triangle \(CEF\).

C:

The slope of line \(\ell\) is equal to the slope of line \(p\).

D:

\(\sin(A) = \sin(C)\)

E:

\(\sin(B) = \cos(C)\)

Solution

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(From Unit 6, Lesson 10.)

Problem 6

Select the equation that states \((x,y)\) is the same distance from \((0,5)\) as it is from the line \(y=\text-3\).

A:

\(x^2+(y+5)^2=(y+3)^2\)

B:

\(x^2+(y-5)^2=(y+3)^2\)

C:

\(x^2+(y+5)^2=(y-3)^2\)

D:

\(x^2+(y-5)^2=(y-3)^2\)

Solution

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(From Unit 6, Lesson 8.)

Problem 7

Select all equations that represent the graph shown. 

Line on a coordinate plane, origin O. Horizontal and vertical scale negative 3 to 4 by 1’s. Points (negative 1 comma 3) and (1 comma 1) are on the line.
A:

\(y=\text-x + 2\)

B:

\((y-3) =\text-(x+1)\)

C:

\((y-3) =\text-x-1\)

D:

\((y-3) = (x-1)\)

E:

\((y+1) =\text-(x-3)\)

Solution

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(From Unit 6, Lesson 9.)

Problem 8

Write a rule that describes this transformation.

original figure image
\((3,2)\) \((6,4)\)
\((4,\text-1)\) \((8,\text-2)\)
\((5,1)\) \((10,2)\)
\((7,3)\) \((14,6)\)

Solution

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(From Unit 6, Lesson 3.)