Question

Determine the coordinates of a point P that is two times closer to B(15, 12) as

it is to A(6, 0). Complete the missing reasons to justify the steps.
2:1
B+A=P(x, y)
P= (12,8)
Determine the weights of the ratio that add to
The point (12, 8) is two times closer to (15,12
it is to (6,0).

Answer 1

To determine the coordinates of point P that is two times closer to B(15, 12) as it is to A(6, 0), we can use the concept of ratios. By assuming a weight of 2 units to 1 unit, we can calculate the coordinates of point P using the given formula. The coordinates of P are (12, 8).

Step-by-step explanation:

To determine the coordinates of point P, we need to find a point that is two times closer to B(15, 12) than it is to A(6, 0). We can use the concept of ratios to solve this problem.

Let's assume that the weight of the ratio is 2 units to 1 unit. This means that for every 2 units of distance from P to B, there is 1 unit of distance from P to A.

Using this ratio, we can calculate the coordinates of point P using the formula:

P(x, y) = ((2 * Ax) + Bx) / (2 + 1), ((2 * Ay) + By) / (2 + 1)

Substituting the values of A(6, 0) and B(15, 12) into the formula, we get:

P(x, y) = ((2 * 6) + 15) / 3, ((2 * 0) + 12) / 3

Simplifying, we find that the coordinates of point P are P(12, 8).

Learn more about Finding the coordinates of a point using the concept of ratios