Find the difference between the points A (a,b) B(-a,-b)
Answers
Answer:
The distance between the points (a, b) and (-a, b) is 2 \sqrt{\left(a^{2}+b^{2}\right)} \text { units }2
(a
2
+b
2
)
units
Solution:
Given, two points are (a, b) and (- a, - b)
We need to find the distance between above two points.
We know that, distance between two points P(x_{1}, y_{1})P(x
1
,y
1
) and Q(x_{2}, y_{2})Q(x
2
,y
2
) is given by:
D(P, Q)=\sqrt{\left(x_{2}-x_{1}\right)^{2}-\left(y_{2}-y_{1}\right)^{2}}D(P,Q)=
(x
2
−x
1
)
2
−(y
2
−y
1
)
2
\text { here, } x_{2}=-a, y_{2}=-b, x_{1}=a \text { and } y_{1}=b here, x
2
=−a,y
2
=−b,x
1
=a and y
1
=b
\text { Now, distance }=\sqrt{(a-(-a))^{2}+(b-(-b))^{2}} Now, distance =
(a−(−a))
2
+(b−(−b))
2
\begin{gathered}\begin{array}{l}{=\sqrt{(a+a)^{2}+(b+b)^{2}}} \\\\ {=\sqrt{(2 a)^{2}+(2 b)^{2}}=\sqrt{4\left(a^{2}+b^{2}\right)}} \\\\ {\text { Distance }=2 \sqrt{\left(a^{2}+b^{2}\right)}}\end{array}\end{gathered}
=
(a+a)
2
+(b+b)
2
=
(2a)
2
+(2b)
2
=
4(a
2
+b
2
)
Distance =2
(a
2
+b
2
)
Hence, the distance between two points is 2 \sqrt{\left(a^{2}+b^{2}\right)} \text { units }2
(a
2
+b
2
)
units