Engineering Questions with Answers - Multiple Choice Questions

# Line Point Distance MCQ’s

1 - Question

The shortest distance between a line and a point is achieved when?
a) a line is drawn at 90 degrees to the given line from the given point
b) a line is drawn at 180 degrees to the given line from the given point
c) a line is drawn at 60 degrees to the given line from the given point
d) a line is drawn at 270 degrees to the given line from the given point

Explanation: The shortest distance between a line and a point is achieved when a line is drawn at 90 degrees to the given line from the given point.

2 - Question

What is the shortest distance between the line given by ax + by + c = 0 and the point (x1,y1)?
a)

b)

c)
d) ax1+by1+c

Explanation: The shortest distance between a line and a point is given by the formula (ax1+by1+c)/(√a2+b2). This formula can be derived using the formula of area of a triangle.

3 - Question

What is the shortest distance between the line given by -2x + 3y + 4 = 0 and the point (5,6)?
a) 4.5 units
b) 5.4 units
c) 4.3 units
d) 3.3 units

Explanation: The shortest distance between a line and a point is given by the formula (ax1+by1+c)/(√a2+b2). Using this formula we get the answer 3.3 units.

4 - Question

What is the general formula for finding the shortest distance between two parallel lines given by ax+by+c1=0 and ax+by+c2=0?
a)

b)

c)
d) c1+c2

Explanation: The general formula for finding the shortest distance between two parallel lines given by ax+by+c1 and ax+by+c2 is (c1-c2)/(√a2+b2). We can find this by considering the distance of any one point on one of the line to the other line.

5 - Question

What is the distance between the lines 3x-4y+7=0 and 3x-4y+5=0?
a) 1 unit
b) 0.5 unit
c) 0.8 unit
d) 0.4 unit

Explanation: As the given lines are parallel so the distance between them can be calculated by using the formula (c1-c2)/(√a2+b2). So we get the distance as 0.4 unit.

6 - Question

What will be the slope of the line given by ax + by + c = 0?
a) -a/b
b) -b/a
c) -c/a
d) a/c

Explanation: The slope of a line given by the equation ax + by + c=0 has the slope of -a/b. So two lines having the same ratio of the coefficient of x and y will be parallel to each other.

7 - Question

What will be the slope of the line given by 10x + 5y + 8=0?
a) -5
b) -2
c) -1.25
d) 5

Explanation: The slope of a line given by the equation ax + by + c=0 has the slope of -a/b. So the slope of the given line will be -2.

8 - Question

What will be the co-ordinates of foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0?
a) (1/5,2/5)
b) (2/25,5/25)
c) (68/25,-49/25)
d) (-49/25,68/25)

Explanation: The foot of perpendicular can be found by equating the distance between the two points and the distance between point and line. This is found to be (68/25,-49/25).

9 - Question

Which of the following is used to find the absolute value of the argument in C++?
a) abs()
b) fabs()
c) mod()
d) ab()

Explanation: In C++ the absolute value of an argument can be found by using the function fabs(). It is available under the header file math.h.

10 - Question

What will be the slope of the line perpendicular to the line 6x-3y-16=0?
a) 1/2
b) -1/2
c) 2
d) -2

Explanation: For two lines to be perpendicular the product of their slopes should be equal to -1. So as the slope of given line is 2 so the slope of line perpendicular to it will be -1/2.

11 - Question

Find the output of the following code.

```#include<math.h>
#include<iostream>
using namespace std;
void distance(float x, float y, float a, float b, float c)
{
float d = fabs((a * x + b * y + c)) / (sqrt(a * a + b * b));
cout<<d;
return;
}
int main()
{
float x = -2;
float y = -3;
float a = 5;
float b = -2;
float c = - 4;
distance(x, y, a, b, c);
return 0;
}```

a) 2.8
b) 1.8
c) 1.4
d) 2.4