Question

Point C(-8,3) divides bar (AB) such that AC:CB is 1:3. If A is located at (-10,9), what are the coordinates of B ?

Answer 1

The coordinates of point B are (-7, 7.5).In this case, C(-8,3) divides line segment AB in the ratio 1:3. Therefore, m = 1 and n = 3. Therefore, the coordinates of point B are (-7, 7.5).

Step-by-step explanation:

To find the coordinates of point B, we need to use the concept of section formula.

The section formula states that the coordinates of a point dividing a line segment in a given ratio can be found using the following formula:

Bx = (Cx * m + Ax * n) / (m + n)

By = (Cy * m + Ay * n) / (m + n)

In this case, C(-8,3) divides line segment AB in the ratio 1:3. Therefore, m = 1 and n = 3.

Substituting the values into the formula, we get:

• Bx = (-8 * 1 + -10 * 3) / (1 + 3) = -28 / 4 = -7
• By = (3 * 1 + 9 * 3) / (1 + 3) = 30 / 4 = 7.5

Therefore, the coordinates of point B are (-7, 7.5).