Question

Find the distance between points (i) G(m+n, m-n) H(m-n, m+n)​

Answer 1

Answer:

GH = $2\sqrt{2}n$

Step-by-step explanation:

We have-

G = (m+n, m-n)

H = (m-n, m+n)

Distance between two points A(a,b) and B(c,d) is given by-

AB = $\sqrt{(a-c)^{2}+(b-d)^{2}}$

So GH = $\sqrt{{m+n)-(m-n)^{2}+{(m-n)(m+n)^{2}}$

GH = $\sqrt{(m+n-m+n)^{2}+(m-n-m-n)^{2}}$

     = $\sqrt{(2n)^{2}+(-2n)^{2}}$

    = $\sqrt{4n^{2}+4n^{2}}$

    = $\sqrt{8n^{2}}$

GH = $2\sqrt{2}n$