Question

Length of the line segments joining the points \[-1-j\] and \[2+3i\] is
(a) -5
(b) 15
(c) 5
(d) 25

Answer 1

Hint: For solving this question you should know about the general information of a line. If any line passes through any points or if it is joining to any two points or if it is joining to any two points then the line equation must satisfy that point. But in this problem we have to give two points and ask for the length of the line. So, we will just find the distance between them. And this gets the length of the line.

Complete step by step answer:
According to the question it is asked to find the length of a line if this joins to points \[-1-j\] and \[2+3i\].
As we know that if any line is joining to any two points then the length of line between them is equal to the distance between them two points. And we use this concept every time when we need to find the length of line between two points.
Here, the given points are \[\left( -1-j \right)\] and \[\left( 2+3i \right)\] we can represent these points as:
Let A be \[\left( -1,-1 \right)\] and \[B\left( 2,3 \right)\]
So, if we count the distance between these two points A & B, then by distance formula,
Distance \[=\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}\]
Here, \[{{x}_{2}}=2,{{x}_{1}}=-1\]
           \[{{y}_{2}}=3,{{y}_{1}}=-1\]
Distance \[AB=\sqrt{{{\left( 2+1 \right)}^{2}}+{{\left( 3+1 \right)}^{2}}}\]
                         \[=\sqrt{9+16}=\sqrt{25}\]
                         \[=5\]

So, the correct answer is “Option c”.

Note: While solving the length of a line which is between two points then always find the distance between them with the help of distance formula. And these distances are equal to the length of the line. And we can use this concept everywhere for real and imaginary both values also.