Mathematics Questions and Answers – Distance of a Point from a Line

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Distance of a Point from a Line”.

1. If equation of a line is y=3x-4 then find the slope of line.
a) 3
b) -3
c) 4
d) -4
View Answer

Answer: a
Explanation: Comparing the above equation with general equation y=m*x + c,
m=3 which is the slope of line.
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2. If equation of line is y=5x+10 then find the value of x-intercept made by the line.
a) 2
b) 1/2
c) -1/2
d) -2
View Answer

Answer: d
Explanation: Given equation is y=5x+10. X-intercept means value of x when y is zero
0=5x+10 => x=-2

3. If equation of line is y=5x+10 then find the value of x-intercept made by the line.
a) 10
b) 1/10
c) -1/10
d) -10
View Answer

Answer: a
Explanation: Given equation is y=5x+10. Y-intercept means value of y when x is zero
y=0+10 => y=10
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4. If equation of a line is 3x+2y-6=0 then x-intercept is _____ and y-intercept is _____
a) 3, 2
b) 2, 3
c) 2, 6
d) 3, 6
View Answer

Answer: b
Explanation: Reducing the above equation to intercept form x/a +y/b =1,
we get x/2 +y/3 =1
a=2 which is x-intercept and b=3 which is y-intercept.

5. If equation of line is x + y=2 then find the perpendicular distance of line from origin.
a) √2
b) √3
c) 1/√2
d) 1/√3
View Answer

Answer: a
Explanation: Given equation is x + y=2. Reducing the above equation to normal form
(x + y)/√2 =√2.
x cos⁡45° + y sin 45° = √2
Perpendicular distance from origin is √2.
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6. If equation of line is x + y=2 then find the angle made by line with x-axis.
a) 45°
b) 60°
c) 30°
d) 75°
View Answer

Answer: a
Explanation: Given equation is x + y=2. Reducing the above equation to normal form
(x + y)/√2 =√2.
x cos⁡45° + y sin 45° = √2
Angle made with x-axis is 45°.

7. Find the equation perpendicular to 2x – y=4 and pass through (2, 4).
a) 2x+y-10 = 0
b) x+2y+10 = 0
c) x+2y-10 = 0
d) x+y-10 = 0
View Answer

Answer: c
Explanation: Line 2x – y=4 has slope 2. Line perpendicular to given line has slope -1/2.
Equation is (y-4) = (-1/2) (x-2)
2y-8 = -x + 2 => x+2y -10 = 0.
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8. Find the equation of line parallel to 4x+y=2 and pass through (2, 5).
a) 4x+y-13=0
b) 4x+y+13=0
c) 4x-y-13=0
d) 4x-y+13=0
View Answer

Answer: a
Explanation: Line 4x+y=2 has slope -4. Line parallel to it has slope -4 and pass through (2, 5) so equation will be y-5 = (-4) (x-2) => 4x+y-13=0

9. Find the perpendicular distance of point (2, 4) from line 2x+y-5=0.
a) \(\frac{6}{\sqrt{5}}\)
b) \(\frac{3}{\sqrt{5}}\)
c) \(\frac{9}{\sqrt{5}}\)
d) \(\frac{3}{\sqrt{2}}\)
View Answer

Answer: b
Explanation: Distance of point (x1, y1) from line ax +by +c=0 is \(|\frac{ax1+by1+c}{\sqrt{a^2+b^2}}|\).
So, distance of point (2, 4) from line 2x+y-5=0 is \(|\frac{2*2+4*1-5}{\sqrt{2^2+1^2}}| = \frac{3}{\sqrt{5}}\).
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10. Find the distance between 2x+y+4=0 and 2x+y+8=0.
a) \(\frac{4}{\sqrt{5}}\)
b) \(\frac{3}{\sqrt{5}}\)
c) \(\frac{9}{\sqrt{5}}\)
d) \(\frac{3}{\sqrt{2}}\)
View Answer

Answer: a
Explanation: Distance between parallel lines ax +by +c1=0 and ax+by+c2=0 is \(|\frac{c1-c2}{\sqrt{a^2+b^2}}|\).
So, distance 2x + y+4=0 and 2x+y+8=0 is \(|\frac{8-4}{\sqrt{2^2+1^2}}|=\frac{4}{\sqrt{5}}\).

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter