Question

Find the distance between two points

(i) P(–6, 7) and Q(–1, –5)

(ii) R(a + b, a – b) and S(a – b, –a – b)

(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`

Answer 1

(i) Here, x_1 = – 6, y_1 = 7 and x_2 = – 1, y_2 = – 5

`PQ=sqrt(((x_2-x_1)^2)+(y_2-y_1)^2)`

`=>PQ=sqrt(((-1+6)^2)+(-5-7)^2)`

`=>PQ=sqrt(25+144)=sqrt169=13`

(ii) We have,

`RS=sqrt((a-b-a-b)^2+(-a-b-a+b)^2)`

`=>RS = sqrt(4b^2+4a^2) = 2sqrt(a^2+b^2)`

(iii) We have,

`AB=sqrt((at_2^2-at_1^2)^2+(2at_2-2at_1)^2`

`=>AB=sqrt(a^2(t_2-t_1)^2(t_2+t_1)^2+4a^2(t_2-t_1)^2)`

`=>AB=a(t_2-t_1)sqrt((t_2+t_1)^2+4)`