Question

The coordinates of points a and b are a(4, −2) and b(12, 10). what are the coordinates of the point that is 14 of the way from a to b?

Answer 1

To find the coordinates of a point that is 14% of the way from point A(4, -2) to point B(12, 10), you can use the following formula:

P(x, y) = (1 - t) * A(x₁, y₁) + t * B(x₂, y₂)

Where:
- P(x, y) is the point you want to find.
- A(x₁, y₁) are the coordinates of point A (4, -2).
- B(x₂, y₂) are the coordinates of point B (12, 10).
- t is the fraction of the distance from A to B.

In this case, t should be 14% or 0.14, as you want the point that is 14% of the way from A to B.

P(x, y) = (1 - 0.14) * (4, -2) + 0.14 * (12, 10)

Now, calculate the coordinates of the point P:

P(x, y) = (0.86 * 4, -2) + (0.14 * 12, 10)

P(x, y) = (3.44, -2) + (1.68, 10)

P(x, y) = (3.44 + 1.68, -2 + 10)

P(x, y) = (5.12, 8)

So, the coordinates of the point that is 14% of the way from A to B are approximately P(5.12, 8).