Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by the point (-1, 6).
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Step-by-Step Solution
Step 1: Define points and ratio
Let the given points be A(−3,10) and B(6,−8). Let the point P(−1,6) divide the line segment AB in the ratio m1:m2. We need to find this ratio.
Step 2: Apply Section Formula for x-coordinate
We use the section formula to find the ratio. We can use either the x -coordinate or the y -coordinate. Let's start with the x -coordinate. Substitute the values x=−1, x1=−3, and x2=6 into the formula.
Step 3: Solve for the ratio using x-coordinates
Substitute the values into the section formula for the x -coordinate. Then, cross-multiply and rearrange the terms to solve for the ratio m1:m2. This gives us the ratio in which the point divides the line segment.
Step 4: Verify with y-coordinate (Optional)
To confirm our ratio, we can also apply the section formula using the y -coordinates. Substitute y=6, y1=10, y2=−8, and the ratio m1:m2=2:7 into the formula. Since both sides of the equation are equal, our ratio is correct.