Question

4. Given the points M(-3, -4) and T(5,0), find the coordinates of the point Q on directed line segment MT that partitions MT in the ratio 2:3.

5. Points A,B and C are collinear on AC, and AB:BC = 3/4. A is located at (x,y), B is located at (4, 1) and C is located at (12, 5). What are the values of x and y?

Answer 1

4 : Coordinate of Q =
`((1)/(5) ,(-12)/(5) )`

5 : Coordinate of point A = (-2,-2)

Explanation :

4) Given the points M(-3, -4) and T(5,0)

x₁= -3, y₁ = -4 and

x₂ = 5, y₂ = 0

m = 2, n = 1

Now apply the section formula,

{(mx₂+nx₁)/(m+n) , (my₂+ny₁)/(m+n)}

Coordinate of point Q =
`((1)/(5) ,(-12)/(5) )`

5) AB:BC = 3:4

A = (x,y), end point

B = (4, 1)

C = (12, 5) end point

So, m = 3 & n = 4

x₁ = x , y₁ = y , x₂=12 & y₂ = 5

Apply section formula we get

4 = (36+4x)/7 & 1 = (15 + 4y)/7

28= 36 + 4x 7 = 4y + 15

4x =-8 4y =-8

x = -2 y = -2