# Lesson 11

Perpendicular Lines in the Plane

- Let’s analyze the slopes of perpendicular lines.

### Problem 1

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

### Problem 2

Match each line with a perpendicular line.

### 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.

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

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

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

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

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

### Problem 4

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

### Problem 5

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

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

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

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

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

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

### Problem 6

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

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

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

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

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

### Problem 7

Select **all** equations that represent the graph shown.

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

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

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

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

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

### Problem 8

Write a rule that describes this transformation.

original figure | image |
---|---|

\((3,2)\) | \((6,4)\) |

\((4,\text-1)\) | \((8,\text-2)\) |

\((5,1)\) | \((10,2)\) |

\((7,3)\) | \((14,6)\) |