Final answer:
The coordinates of the point that divides the line segment from (-8,4) to (-3,9) in a 3 to 2 ratio are (-5, 7), found using the section formula.
Step-by-step explanation:
The student has asked for the coordinates of a point that divides the line segment from (-8,4) to (-3,9) into a ratio of 3 to 2. To find this point, we can use the formula for the section formula in coordinate geometry, which gives the coordinates (x, y) of a point that divides a line segment between two given points (x1, y1) and (x2, y2) into a ratio m:n:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
With the coordinates of the points (-8, 4) and (-3, 9) and the ratio of 3 to 2, we can substitute these values into the formula:
x = (3 * (-3) + 2 * (-8)) / (3 + 2)
y = (3 * 9 + 2 * 4) / (3 + 2)
Now calculate the values:
x = (-9 - 16) / 5
y = (27 + 8) / 5
x = -25 / 5
y = 35 / 5
x = -5
y = 7
Therefore, the coordinates of the point that divides the directed line segment in a 3:2 ratio are (-5, 7).