The endpoints of line segment XY are X(-6,2) and Y(6,-10). Find the point Q the partitions YX in a ratio of 3:1
the point is 3/4 of the distance from Y to X
the points are 12 units apart in the X and Y directions
... so, 9 units from Y toward X
To find the point Q that divides line segment YX in a ratio of 3:1, we need to use the section formula.
The section formula states that for a line segment with endpoints A(x1, y1) and B(x2, y2), dividing it in the ratio of p:q will result in a point Q with coordinates (x, y), where:
x = (px2 + qx1) / (p + q)
y = (py2 + qy1) / (p + q)
In this case, point X is given as X(-6, 2) and point Y is given as Y(6, -10). We want to divide line segment YX in a ratio of 3:1, so p = 3 and q = 1.
Let's substitute the values into the section formula to find point Q:
x = (3 * 6 + 1 * (-6)) / (3 + 1)
= (18 - 6) / 4
= 12 / 4
= 3
y = (3 * (-10) + 1 * 2) / (3 + 1)
= (-30 + 2) / 4
= -28 / 4
= -7
Therefore, the point Q that partitions YX in a ratio of 3:1 is Q(3, -7).