Question

I need help with this please​

Answer 1

In general the segment from A to B has parametric equation

X = (1-t)A + tB

t=0 gives point A, t=1 gives point B, and in between we move linearly with t from A to B.

So if we want AX:BX=1:3, that's 1/(1+3)=1/4 of the way along from A to B, so corresponds to t=1/4. So the point we seek is

X = (1 - 1/4)(3, 2) + (1/4)(6,8) = ((9+6)/4, (6+8)/4)=(15/4, 7/2)

Answer: Choice C

Answer 2

D

Explanation:

The difference in the x-coordinates is Δx = 6 - 3 = 3.

The difference in the y-coordinates is Δy = 8 - 2 = 6.

One third the difference is Δx/3 = 3/3 = 1 and Δy/3 = 6/3 = 2.

So the one-third point is at (3 + 1, 2 + 2) = (4, 4).