X is a point between A(-5,-2) and B(5,13) such that AX:XB = 2:3. Find the coordinates of X.
To find the coordinates of point X, we will use the concept of section formula or internal division.
Let's label the coordinates of point X as (x, y).
According to the given information, the ratio of AX to XB is 2:3. This means that if we divide the line segment AB into two parts, the length of AX is 2 times the length of XB.
To determine the coordinates of point X, we can use the section formula:
For a line segment with endpoints (x1, y1) and (x2, y2), divided into parts in the ratio of m:n, the coordinates of the dividing point are given by:
x = (n * x1 + m * x2) / (m + n)
y = (n * y1 + m * y2) / (m + n)
Using the section formula, we can substitute the coordinates of points A(-5, -2) and B(5, 13) into the formula to calculate the coordinates of point X.
x = (3 * (-5) + 2 * 5) / (2 + 3)
y = (3 * (-2) + 2 * 13) / (2 + 3)
Simplifying these equations will give us the coordinates of point X.