# PARALLEL AND PERPENDICULAR LINES WORKSHEET

## About "Parallel and perpendicular lines worksheet"

Parallel and perpendicular lines worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on parallel and perpendicular lines.

## Parallel and perpendicular lines worksheet - Problems

Problem 1 :

Think of each segment in the diagram as part of a line. Which of the lines appear to fit the descriptions given below ?

(i) Parallel to AB and contains D

(ii) Perpendicular to AB and contains D

(iii) Skew to AB and contains D

(iv) Name the plane(s) that contain D and appear to be parallel to plane ABE.

Problem 2 :

In the diagram given below, lines m, n and k represent three of the oars. If m||n and n||k, then prove m||k. Problem 3 :

In the diagram given below, find the slope of each line. Determine whether the lines jand jare parallel. Problem 4 :

In the diagram given below,

Line n1 has the equation y  =  -x/3 -1.

Line n2 is parallel to the line n1 and passes through the point (3, 2).

Write the equation of the line n2. Problem 5 :

Decide whether the lines are perpendicular.

Line 1 : y = 3x/4 + 2

Line 2 : y = -4x/3 - 3

Problem 6 :

In the diagram given below, the equation y = 3x/2 + 3 represents a mirror. A ray of light hits the mirror at (-2, 0). What is the equation of the line p that is perpendicular to the mirror at this point ?  ## Parallel and perpendicular lines worksheet - Solution

Problem 1 :

Think of each segment in the diagram as part of a line. Which of the lines appear to fit the descriptions given below ?

(i) Parallel to AB and contains D

(ii) Perpendicular to AB and contains D

(iii) Skew to AB and contains D

(iv) Name the plane(s) that contain D and appear to be parallel to plane ABE.

Solution (i) :

CD, GH and EF are all parallel to AB. But, only CD passes through D and is parallel to AB.

Solution (ii) :

BC, AD, AE and BF are all perpendicular to AB. But, only AD passes through D and is perpendicular to AB.

Solution (iii) :

DG, DH and DE all pass through D and are skew to AB.

Solution (iv) :

Only plane DCH contains D and is parallel to plane ABE.

Problem 2 :

In the diagram given below, lines m, n and k represent three of the oars. If m||n and n||k, then prove m||k. Solution :

 Statementsm||n∠1 ≅ ∠2n||k∠2 ≅ ∠3∠1 ≅ ∠3m||k ReasonsGivenCorresponding angles postulateGivenCorresponding angles postulateTransitive property of congruenceCorresponding angle converse

Problem 3 :

In the diagram given below, find the slope of each line. Determine whether the lines jand jare parallel. Solution :

Line j1 has a slope of

m2  =  4/2  =  2

Line j2 has a slope of

m2  =  2/1  =  2

Since the slope of the lines jand jare equal, the lines jand jare parallel.

Problem 4 :

In the diagram given below,

Line n1 has the equation y  =  -x/3 -1.

Line n2 is parallel to the line n1 and passes through the point (3, 2).

Write the equation of the line n2. Solution :

The slope of the line n1 is -1/3. Because the lines n1 and n2 are parallel, they have the same slope. So, the slope of the line n2 is also -1/3.

Slope-intercept form equation of a line :

y  =  mx + b ------(1)

Because the line n2 is passing through (3, 2), substitute aa(x, y)  =  (3, 2) amd m  =  -1/3

2  =  (-1/3)(3) + b

Simplify

2  =  -1 + b

Add 1 to both sides.

3  =  b

The equation of the required line is

(1) ------> y  =  (-1/3)x + 3

y  =  -x/3 + 3

Problem 5 :

Decide whether the lines are perpendicular.

Line 1 : y = 3x/4 + 2

Line 2 : y = -4x/3 - 3

Solution :

When we compare the given equations to slope intercept equation of a line y = mx + b, we get

slope of line 1  =  3/4

slope of line 2  =  -4/3

Multiply the slopes :

The product is

= (3/4) x (-4/3)

= - 1

Since the product of slopes of the lines is -1, the given lines are perpendicular.

Problem 6 :

In the diagram given below, the equation y = 3x/2 + 3 represents a mirror. A ray of light hits the mirror at (-2, 0). What is the equation of the line p that is perpendicular to the mirror at this point ? Solution :

The slope of the mirror is 3/2. So, the slope of the line p is -2/3.

Let y = mx + b be the equation of the line p.

Substitute (x, y)  =  (-2, 0) and m  =  -2/3 to find the value of b.

0  =  (-2/3)(-2) + b

0  =  4/3 + b

Subtract 4/3 from both sides.

-4/3  =  b

So, the equation of the line p is

y  =  -2x/3 - 4/3 After having gone through the stuff given above, we hope that the students would have understood "Parallel and perpendicular lines worksheet".

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