# Lesson 11

Perpendicular Lines in the Plane

### 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.

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:

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

### 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

(From Unit 6, Lesson 10.)

### Problem 5

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

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

(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

(From Unit 6, Lesson 8.)

### Problem 7

Select all equations that represent the graph shown.

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

(From Unit 6, Lesson 9.)

### Problem 8

Write a rule that describes this transformation.

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