Question

let A(p+q, pq) and B(pq, p+q) be pointed in a Cartesian plane. Then AB^2 = .... sq units
a) 2q
b) 2√2q^2
c) 2q^2
d) None of these
Note*- answer with complete process and steps

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Points are A(p+q,pq) and B(pq, p+q)}$

$\underline{\textbf{To find:}}$

$\textsf{The distance between A and B}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Formula used:}}$

$\mathsf{The\;distance\;between\;the\;points\;(x_1,y_1)\;and\;(x_2,y_2)\;is}$

$\boxed{\mathsf{d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}}}$

$\textsf{The distance between A(p+q,pq) and B(pq, p+q)}$

$\mathsf{=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}}$

$\mathsf{=\sqrt{(p+q-pq)^2+(pq-(p+q))^2}}$

$\mathsf{But,\;\;(a-b)^2=(b-a)^2}$

$\mathsf{=\sqrt{(p+q-pq)^2+(p+q-pq)^2}}$

$\mathsf{=\sqrt{2\,(p+q-pq)^2}}$

$\mathsf{=\sqrt{2}(p+q-pq)}$

$\underline{\textbf{Answer:}}$

$\mathsf{Option\;(d)\;is\;correct}$

$\underline{\textbf{Find more:}}$

P(5,-3) and Q(-7,y) and PQ=13 units, find y​  

https://brainly.in/question/15041779

Find the distance CD where c (-3 a, a) D(a , -2 a )​

https://brainly.in/question/38177565  

Answer 2

Answer:

Option D is the correct answer.