The line segment joining ( -3,-4) and (6,11) is to be divided in to three (3) equal parts. Find the coordinates of the point of the part closest to (-3,-4).

The x- and y- changes from the first point to the last are 9 and 15

So, add 1/3 of those values to the first point.

Thanks... :)

To find the coordinates of the point on the line segment closest to (-3,-4) when dividing it into three equal parts, you can use the concept of finding a point on a line segment using the section formula.

The section formula states that if we have two points (x1, y1) and (x2, y2) on a line segment, and we want to divide the line segment in a ratio of m:n, then the coordinates of the point dividing the line segment in that ratio can be found using the following formulas:

x = (n * x1 + m * x2) / (m + n)
y = (n * y1 + m * y2) / (m + n)

In this case, we want to divide the line segment into three equal parts, so the ratio is 1:2. The given points are (-3,-4) and (6,11).

Using the section formula:

x = (2 * (-3) + 1 * 6) / (1 + 2)
= (-6 + 6) / 3
= 0 / 3
= 0

y = (2 * (-4) + 1 * 11) / (1 + 2)
= (-8 + 11) / 3
= 3 / 3
= 1

Therefore, the coordinates of the point closest to (-3,-4) is (0, 1).