PERPENDICULAR LINES IN THE COORDINATE PLANE WORKSHEET

Problem 1 :

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

Problem 2 :

In the diagram given below, find the slope of each line. Determine whether the lines are perpendicular.

Problem 3 :

Decide whether the lines are perpendicular.

Line 1 : y = 3x/4 + 2

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

Problem 4 :

Decide whether the lines are perpendicular.

Line 1 : 4x + 5y = 2

Line 2 : 5x + 4y = 3

Problem 5 :

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 ?

1. Answer :

Part 1 :

Find the slope of the line j1. Line j1 is passing through the points (0, 3) and (3, 1).

Let (x1, y1) = (0, 3) and (x2, y2) = (3, 1).

Slope (j1) = (y2 - y1)/(x2 - x1)

Slope (j1) = (1 - 3)/(3 - 0)

Slope (j1) = -2/3

Part 2 :

Find the slope of the line j2. Line j2 is passing through the points (0, 3) and (-4, -3).

Let (x1, y1) = (0, 3) and (x2, y2) = (-4, -3).

Slope (j2) = (-3 - 3)/(-4 - 0)

Slope (j2) = -6/(-4)

Slope (j2) = 3/2

Multiply the slopes :

The product is

= (-2/3) x (3/2) 

= -1

Since the product of slopes of the lines j1 and jis -1, the lines  j1 and j2 are perpendicular.

2. Answer :

Part 1 :

Find the slope of the line AC. Line AC is passing through the points (1, -4) and (4, 2).

Let (x1, y1) = (1, -4) and (x2, y2) = (4, 2).

Slope of AC = (y2 - y1)/(x2 - x1)

= [(2 - (-4)]/(4 - 1)

= (2 + 4)/3

= 6/3

2

Part 2 :

Find the slope of the line BD. Line BD is passing through the points (-1, 2) and (5, -1).

Let (x1, y1) = (-1, 2) and (x2, y2) = (5, -1).

Slope of BD = (-1 - 2)/[(5 - (-1)]

-3/6

= -1/2

Multiply the slopes :

The product is

= 2 x (-1/2) 

= -1

Since the product of slopes of the lines is -1, the lines  AC and BD are perpendicular.

3. Answer :

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.

4. Answer :

Rewrite each equation in slope-intercept form to find the slope. 

Line 1

4x + 5y = 2

5y = -4x + 2

y = -4x/5 + 2/5

Slope = -4/5

Line 2

5x + 4y = 3

4y = -5x + 3

y = -5x/4 + 3/4

Slope = -5/4

Multiply the slopes :

The product is

= (-4/5) x (-5/4)

= 1

Since the product of slopes of the lines is not -1, the given lines  are not perpendicular.

5. Answer :

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

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