Question

Point Q is on MN such that MQ:QN 2:3. If M has coordinates (3,5) and N has coordinates (8, -5), the coordinates of Q are

A) (5,1)
B) (5,0)
C) (6,-1)
D) (6,0)

Answer 1

Option A. (5, 1)

Explanation:

Let the coordinates of the point Q be (X, Y).

Coordinates of M and N are (3, 5) and (8, -5).

Point Q divides the line segment MN in two parts MQ : QN :: 2 : 3

Or ratio of MQ and QN is 2 : 3

Now we know the formula

X = x +
`(a)/(a+b)(x'-x)`

and Y = y +
`(a)/(a+b)(y'-y)`

here a and b is the ration in which line MN is divided.

For x coordinates

X = 3 +
`(2)/(2+3)(8-3)`

X = 3 +
`(2)/(5)(5)`

X = 3 + 2 = 5

Now for y coordinates

Y = 5 +
`(2)/(2+3)(-5-5)`

Y = 5 +
`((2)(-10))/(5)`

Y = 5 - 4

Y = 1

Therefore, coordinates of Q are Option A. (5, 1).

Answer 2

We determine the coordinates of point Q by getting the difference or the distance between the coordinates of the points given and multiply by the ratio.
(x-component) (8 - 3) x 2/5 = 2 : 3 + 2 = 5
(y - component) (-5 - 5) x 2/5 = -4 : 5 + -4 = 1

Thus, the coordinates of Q are (5,1). The answer is A.