Question

(b) Show that P(3, m-5) is a point of trisection of the line segment joining the points
A (4,-2) and B(1,4). Hence find the value of m.​

Answer 1

Step-by-step explanation:

formula

p(x, y)=(mx2+nx1/m+n, my2+ny1/m+n)

p(3, m-5)=(1*1+2*4/1+2, 1*4+2*-2/1+2)

= (1+8/3, 4-4/3)

=(9/3, 0/3)

corresponding coordinates are equal

m-5=0

m=5

Answer 2

The value of m is equal to 5.

Given that the point P(3,m-5) is a point of trisection of the line segment joining the points A(4,-2) and B(1,4).

The ratio AP:PB is equal to 1:2 as the point P is the point of trisection of the line AB.

Using the section formula to find the value of m-

m-5 = (4 × 1 + (-2) × 2)/3

=> 3m - 15 = 0

=> m = 5

The value of m is equal to 5.