136k views
0 votes
Point A is at (-2, 4) and point C is at (4, 7). Find the coordinates of point B on AC such that the ratio of AB to AC is 1: 3.

User CYAD
by
6.3k points

1 Answer

6 votes

Answer:

Explanation:

To find the coordinates of point B on line segment AC such that the ratio of AB to AC is 1:3, we need to find a point that is one-fourth of the way from point A to point C.

One way to find the point is to use the midpoint formula:

Let the coordinates of point B be (x, y). Then, the midpoint of line segment AB is:

x = (x1 + x2)/2 and y = (y1 + y2)/2,

where x1 and y1 are the coordinates of point A and x2 and y2 are the coordinates of point B.

Setting x1 = -2 and y1 = 4, and x2 = x and y2 = y, we can solve for x and y:

x = (-2 + x)/2 and y = (4 + y)/2

Next, we can set the midpoint equal to the point that is one-fourth of the way from point A to point C, which can be found by averaging the coordinates of point A and C:

x = (-2 + 4)/4 = 1 and y = (4 + 7)/4 = 5.5

So, the coordinates of point B are (1, 5.5).

User Ilovecomputer
by
7.9k points