Final answer:
To find the coordinates of point B on AC such that the ratio is 1:3, use the midpoint formula to find the midpoint of AC. Then, use the distance formula to find the distance between point A and the midpoint. Lastly, use the section formula to find the coordinates of point B.
Step-by-step explanation:
To find the coordinates of point B on AC such that the ratio is 1:3, we can use the concept of midpoint formula. First, find the midpoint of AC using the formula: (x1 + x2) / 2, (y1 + y2) / 2. Substitute the coordinates of point A (-2,4) and point C (4,7) into the formula to find the midpoint. The midpoint is (1, 5.5).
Next, find the distance between point A and the midpoint using the distance formula: √((x2 - x1)² + (y2 - y1)²). Substitute the coordinates of point A (-2,4) and the midpoint (1, 5.5) into the formula to find the distance. The distance is √26.5.
Now, since the ratio is 1:3, we can find the coordinates of point B using the concept of section formula. The coordinates of point B are: ((3 * x1) + x2) / 4, ((3 * y1) + y2) / 4. Substitute the coordinates of point A (-2,4) and the midpoint (1, 5.5) into the formula to find the coordinates of point B which are (-0.25, 4.625).