The line segment connecting A(-18,8) and B(-10,-8) is divided in the ratio 1:3 by point C. The coordinates of C are...
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C is 1/4 of the way from A to B.
So, add 1/4 of the difference in coordinates (B-A) to A:
C = (-18,8)+(2,-4) = (-16,4)
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To find the coordinates of point C, you can use the concept of dividing a line segment in a given ratio.
Step 1: Calculate the difference between the x-coordinates and y-coordinates of points A and B.
Δx = x₂ - x₁ = -10 - (-18) = -10 + 18 = 8
Δy = y₂ - y₁ = -8 - 8 = -16
Step 2: Calculate the x-coordinate of point C.
x-coordinate of C = (ratio * Δx + x₁) / (ratio + 1) = (1 * 8 + (-18)) / (1 + 3) = (8 - 18) / 4 = -10 / 4 = -2.5
Step 3: Calculate the y-coordinate of point C.
y-coordinate of C = (ratio * Δy + y₁) / (ratio + 1) = (1 * (-16) + 8) / (1 + 3) = (-16 + 8) / 4 = -8 / 4 = -2
Therefore, the coordinates of point C are (-2.5, -2).