The ratio in which point T(–1, 6)divides the line segment joining the points P(–3, 10) and Q(6, –8). is 2:7.
We can use the section formula to find the ratio in which point T(–1, 6) divides the line segment joining the points P(–3, 10) and Q(6, –8). The section formula states that if a point divides a line segment in the ratio k:m, then the coordinates of the point are given by:
(x, y) = (mx2 + kx1)/(m + k), (my2 + ky1)/(m + k)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.
In this case, we have:
(x1, y1) = (–3, 10)
(x2, y2) = (6, –8)
(x, y) = (–1, 6)
Plugging these values into the section formula, we get:
(–1, 6) = (6m – 3k)/(m + k), (–8m + 10k)/(m + k)
Solving for m and k, we get:
m = 7
k = 2
Therefore, the ratio in which point T(–1, 6) divides the line segment joining the points P(–3, 10) and Q(6, –8) is 2:7.