Question

Given AC with A(3, 4) and C(-9, -2), if B partitions AC such that the ratio of AB to BC is 1:5, find the coordinates of B.

Answer 1

To find the coordinates of point B on line AC, we need to use the concept of partitioning a line segment with a given ratio. By calculating the x and y coordinates of B using the ratio, we can determine the coordinates of B as (-1, 3).

Step-by-step explanation:

To find the coordinates of point B, we can use the concept of partitioning a line segment.

Let's calculate the coordinates of B by finding the ratio of AB to BC. The given ratio is 1:5.

First, find the x-coordinate of B using the formula:
Bx = (5*Ax + 1*Cx) / (1 + 5) = (5*3 + 1*(-9)) / 6

Then, find the y-coordinate of B using the formula:
By = (5*Ay + 1*Cy) / (1 + 5) = (5*4 + 1*(-2)) / 6

Therefore, the coordinates of B are (−1, 3).