Question

What are the coordinates of the point on the directed line segment from (-5,3) to (5,8) that partitions the segment into a ratio of 3 to 2?

Answer 1

1,6

Explanation:

From -5 to +5 (for x) is 10 we need 3/ ( 2+3) ths of this = 6

-5 + 6 = 1

for y from 3 to 8 is 5 we need 3/5ths of this = 3 added to 3 = 6

Answer 2

(1, 6)

Explanation:

Definitions:

• Let A = (-5, 3)
• Let B = (5, 8)
• Let M be the required point.

Given ratio 3 : 2.

Therefore, point M is ³/₅ along the line from point A to point B.

`\begin{aligned}\implies x_M&=(3)/(5)(x_B-x_A)+x_A\\&=(3)/(5)(5-(-5))+(-5)\\&=(3)/(5)(10)-5\\&=1\end{aligned}`

`\begin{aligned}\implies y_M&=(3)/(5)(y_B-y_A)+y_A\\&=(3)/(5)(8-3)+3\\&=(3)/(5)(5)+3\\&=6\end{aligned}`

Therefore, point M is (1, 6).