Final answer:
To find the coordinates of point T that divides the line segment between points A(-2, 1) and B(8, 11) in a 2:3 ratio, we use the section formula and find the coordinates to be (2, 5).
Step-by-step explanation:
To find the coordinates of point T that divides the line segment between A(-2, 1) and B(8, 11) in a 2:3 ratio, we apply the section formula in coordinate geometry.
To find the coordinates of the point T(x, y), we use the formula:
T(x, y) = ((m×x2 + n×x1) /(m + n), (m×y2 + n×y1) / (m + n))
Where A(x1, y1), B(x2, y2), and m:n is the given ratio.
Let's plug in the values into the formula:
- m = 2 and n = 3 for the given 2:3 ratio.
- A(-2, 1), where x1 = -2 and y1 = 1.
- B(8, 11), where x2 = 8 and y2 = 11.
The formula gives us:
- x-coordinate of T = (2×8 + 3×(-2)) / (2 + 3) = (16 - 6) / 5 = 10 / 5 = 2
- y-coordinate of T = (2×11 + 3×1) / (2 + 3) = (22 + 3) / 5 = 25 / 5 = 5
So, the coordinates of point T are (2, 5).