Question

What is 2/3 of (-2,9) to (5,-1)

Answer 1

Therefore 2/3 of (-2,9) to (5,-1) =
`(2)/(3) * √(149)` = 8.138

Explanation:

i) the given two points
`(x_(1) , y_(1))` and
`(x_(2) , y_(2))` are given as (-2, 9) and (5,-1) respectively.

ii) the given section mentioned above is to be divided in the ratio 2/3.

iii) the formula to find the point (x, y) which divides a line segment in the ratio m:n is given by

x =
`(mx_(2) + nx_(1))/(m + n)` =
`((2 * 5) + (3 * -2) )/(2 + 3)` =
`(4)/(5)` and y =
`(my_(2) + ny_(1))/(m + n)`=
`((2 * -1) + (3 * 9) )/(2 + 3)` = 5

iv) The distance between the two points
`(x_(1) , y_(1))` and
`(x_(2) , y_(2))` are given as (-2, 9) and (5,-1) =
`\sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)} = \sqrt{(5 - (-2))^(2) + (-1 - 9)^(2)} = \sqrt{7^(2) + (-10)^(2) } = √(49 + 100) = √(149)`v) Therefore 2/3 of (-2,9) to (5,-1) =
`(2)/(3) * √(149)` = 8.138