Question

Given a segment AB with A at (3,4) and B at (-7,8), what are the coordinates of the point that is 3/4 of the way from A to B?

a) (0,6)
b) (1,5)
c) (-5,7)
d) (-4,7)

Answer 1

To find the point that is 3/4 of the way from A to B, use the formula for finding a point on a line segment and substitute the given values.

Step-by-step explanation:

To find a point that is 3/4 of the way from point A to point B, we can use the formula for finding a point along a line segment. The formula is:

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

Given that A is (3,4) and B is (-7,8), and we want to find a point that is 3/4 of the way, we can let t = 3/4. Plugging the values into the formula:

(x, y) = ((1 - 3/4) * 3 + (3/4) * -7, (1 - 3/4) * 4 + (3/4) * 8)

Simplifying:

(x, y) = (0, 6)

Therefore, the coordinates of the point that is 3/4 of the way from A to B are (0,6).