Final answer:
Using the section formula, the point dividing the line segment between (10, -4) and (-6, 4) in a 5:3 ratio is (0, 1).
Step-by-step explanation:
To find the point that divides the line segment between the points (10, -4) and (-6, 4) into a ratio of 5:3, we can use the section formula. This formula involves averaging the x-coordinates and y-coordinates separately, weighted by the ratio, to find the coordinates of the dividing point (x, y). The section formula states that if a line segment AB is divided by a point P in the ratio m:n, then the coordinates of P are given by:
((m * x2 + n * x1) / (m + n), (m * y2 + n * y1) / (m + n))
Applying this formula to our specific question:
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- m = 5 (for the first part of the ratio)
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- n = 3 (for the second part of the ratio)
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- x1, y1 = (10, -4) (coordinates of the first point)
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- x2, y2 = (-6, 4) (coordinates of the second point)
Now, let's calculate it:
x = (5*(-6) + 3*10) / (5 + 3)
y = (5*4 + 3*(-4)) / (5 + 3)
x = (-30 + 30) / 8 = 0/8 = 0
y = (20 - 12) / 8 = 8/8 = 1
Therefore, the point that divides the line segment between (10, -4) and (-6, 4) into a ratio of 5:3 is (0, 1).