Question

Find the distance between the points (a,a) and (2a,2a)​

Answer 1

Formula to find the distance between two points is given by -

`\small \underline{ \boxed{ \sf{ \pmb{ Distance = √( (y_2 -y_1)^2 + (x_2-x_1)^2)}}}}\\`

As per question, points are -

• A (a,a)

• B(2a,2a)

On substituting the values :-

`\longrightarrow \sf {Distance(AB) = √( (2a-a)^2 + (2a-a)^2 )}\\`

`\longrightarrow \sf {Distance (AB)= √( a^2 + a^2 )}\\`

`\longrightarrow \sf {Distance(AB) = √( 2a^2 )}\\`

`\longrightarrow \sf {Distance (AB)= √( 2) * √(a^2 )}\\`

`\longrightarrow \sf {Distance(AB) = √( 2) * a }\\`

`\longrightarrow \boxed{ \tt{ \pmb{ \red{Distance(AB) = √( 2) * a }}}}\\`

`\\ \therefore \underline{ \cal{ \pmb{The \:distance \: of \: the\: two \:points \: is \: \frak{\purple{ √(2)* a}. }}}}\\`