Question

What are the coordinates of point B on AC such that the ratio of AB to

BC is 2: 3?
Choose 1 answer:
B
3-
-7-6-5-4-3-2 +
A 2+
3 3
8
3-
5+
5' 5
A
3-
2+
-
T
-3+
(2²/1/3, 1/2)
5
(2¹,1)
3 3
44
A
-5
6
1
2 3 4 5 6 7
C

Answer 1

So, the coordinates of point B are (3.2, -0.2).

Explanation:

To find the coordinates of point B on AC such that the ratio of AB to BC is 2:3, we can use the concept of section formula.

The coordinates of point A are (2, 3), and the coordinates of point C are (5, -5).

Let the coordinates of point B be (x, y).

The ratio of AB to BC is 2:3, which means:

AB/BC = 2/3

Using the section formula, we can write:

x = (3 * 2 + 2 * 5) / (2 + 3) = (6 + 10) / 5 = 16 / 5 = 3.2

y = (3 * 3 + 2 * (-5)) / (2 + 3) = (9 - 10) / 5 = -1 / 5 = -0.2

So, the coordinates of point B are (3.2, -0.2).

Answer 2

`\sf A. \left( 2(1)/(5), (1)/(5)\right)`

Explanation:

In order to find the coordinates of point B on segment AC such that the ratio of AB to BC is 2:3, we can use the concept of the section formula. The section formula states that if a point B divides a line segment AC in the ratio of m:n, then the coordinates of point B are given by :

`\sf B\left((mx_2 + nx_1)/(m + n), (my_2 + ny_1)/(m + n)\right)`

In this case:

Point A has coordinates (-1, -1), and point C has coordinates (7, 2).

We want to find point B such that AB:BC = 2:3, which means m:n = 2:3.

So, m = 2 and n = 3.

Now, use the section formula to find the coordinates of point B:

`\sf B\left((2(7) + 3(-1))/(2 + 3), (2(2) + 3(-1))/(2 + 3)\right)`

Simplify:

`\sf B\left((14 - 3)/(5), (4 - 3)/(5)\right)`

`\sf B\left((11)/(5), (1)/(5)\right)`

`\sf B\left( 2(1)/(5), (1)/(5)\right)`

So, the coordinates of point B on segment AC are:

`\sf A. \left( 2(1)/(5), (1)/(5)\right)`