Perpendicular lines are two separate lines that meet each other at 90-degree angle. If two lines are perpendicular then their slopes are the reciprocals of each other and its product is equal to -1.
Question 1: What line is perpendicular to 4x+3y=12 and passes through (4,2)?
(a) 4x-3y=12
(b) 3x-4y= 1
(c) 4x-3y=1
(d) 2x+3y=12
Answer: (b)
Explanation: The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.
Question 2: If a line has an equation of 2y=5x+12, what is the slope of a line that is perpendicular to the line?
(a) 5/2
(b) -5/2
(c) -2/5
(d) 2/5
Answer: (c)
Explanation: The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.
Question 3: Which of the following is possibly a line perpendicular to 10y=5x+32 ?
(a) 5x+10y = 45
(b) 10x+5y = 52
(c) 10x-5y = 12
(d) -6x + 10y = 12
Answer: (b)
Explanation: The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.
Question 4: Find the equation of line perpendicular to the line y =3x+7 and has a y- intercept of -2?
(a) x+3y+2 = 0
(b) x- 3y-2 = 0
(c) 3x+y + 2 =0
(d) 3x-y-2 = 0
Answer: (a)
Explanation: The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.
Question 5: What is the slope of the line perpendicular to the line given by the equation
9x – 6y +14 = 0
(a) -2/3
(b) 2/3
(c) 3/2
(d) -3/20
Answer: (a)
Explanation: The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.
Question 6: What is the slope of a line that is perpendicular to the equation given by:
y=4x−6?
(a) m=4
(b) m=0
(c) m=1
(d) m=1/4
Answer: (d)
Explanation: Perpendicular lines have slopes whose product is -1.
Question 7: What is the slope of a line perpendicular to line D, which runs through (5,0)and (7,0)?
(a) 5/7
(b) -5/7
(c) 7/5
(d) Slope is undefined
Answer: (d)
Explanation: Slope of the line (5,0) and (7,0)
m= (0-0)/(7-5)= 0/2 = 0
Question 8: Are the following two lines parallel, perpendicular, or neither:
y=−1x+2 and y=1x+7
(a) They are parallel
(b) They are perpendicular
(c) They are neither parallel nor perpendicular
(d) None
Answer: (b)
Explanation: y=−1x+2, Slope,n = -1
and y=1x+7, slope,m = 1
Question 9: Find the equation of the line which is perpendicular to y=4x−6 and passes through (-2,2)?
(a) 4x-y+10=0
(b) 4x+4y+10=0
(c) x-4y-10=0
(d) x+4y-10=0
Answer: (d)
Explanation: The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.
Question 10: What is the slope of a line perpendicular to line D, which runs through (3,1)and (7,2)?
(a) 2
(b) 3/2
(c) -2
(d) -3/2
Answer: (c)
Explanation: Slope of the line (3,1) and (7,2)
m= (2-1)/(7-5)= 1/2 = 1/2
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