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

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. 

Answer 2

Answer:

Option A. (5, 1)

Step-by-step 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 + $\frac{a}{a+b}(x'-x)$

and Y = y + $\frac{a}{a+b}(y'-y)$

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

For x coordinates

X = 3 + $\frac{2}{2+3}(8-3)$

X = 3 + $\frac{2}{5}(5)$

X = 3 + 2 = 5

Now for y coordinates

Y = 5 + $\frac{2}{2+3}(-5-5)$

Y = 5 + $\frac{(2)(-10)}{5}$

Y = 5 - 4

Y = 1

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