Coordinate Geometry
Distance Formula
NCERT Exercise
7.1 Part 1
Question: 1 - Find the distance between the following pairs of points:
(i) (2,3), (4,1)
Answer: Let (x1, y1) = (2, 3) and (x2, y2) = (4, 1)
We know that distance formula
`=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
`=sqrt((4-2)^2+(1-3)^2)`
`=sqrt(2^2+-2^2)`
`=sqrt(4+4)`
`=sqrt8=2sqrt2` units
(ii) (-5, 7), (-1, 3)
Answer: Let (x1, y1) = (-5, 7) and (x2, y2) = (-1, 3)
We know that distance formula
`=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
`=sqrt((-1+5)^2+(3-7)^2)`
`=sqrt((-4)^2+(-4)^2)`
`=sqrt(16+16)`
`=sqrt(32)=4sqrt2` units
(iii) (a, b), (-a, -b)
Answer: Let (x1, y1) = (a, b) and (x2, y2) = (-a, -b)
We know that distance formula
`=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
`=sqrt((-a-a)^2+(-b-b)^2)`
`=sqrt((-2a)^2+(-2b)^2)`
`=sqrt(4a^2+4b^2)`
`=sqrt(4(a^2+b^2)`
`=2sqrt(a^2+b^2)` units