232k views
3 votes
If A (4,1) and B (-3,0), find the point that divides AB two-thirds of the way from A to B.

User Parvina
by
8.3k points

1 Answer

4 votes

Final answer:

The point that divides AB two-thirds of the way from A to B is (-2/3, 1/3).

Step-by-step explanation:

To find the point that divides AB two-thirds of the way from A to B, we can use the section formula. The section formula states that the coordinates of the point dividing a line segment with endpoints (x1, y1) and (x2, y2) into two parts with ratios m:n are given by:

x = (m*x2 + n*x1) / (m + n)

y = (m*y2 + n*y1) / (m + n)

In this case, A has coordinates (4,1), B has coordinates (-3,0), and we want to divide AB two-thirds of the way from A to B, so m = 2 and n = 1. Plugging in these values, we get:

x = (2*-3 + 1*4) / (2 + 1) = -2/3

y = (2*0 + 1*1) / (2 + 1) = 1/3

Therefore, the point that divides AB two-thirds of the way from A to B is (-2/3, 1/3).

User Fastcatch
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories