Find the ratio in which the point (−1,k) divides the line segment joining the points (−3,10) and (6,−8). Hence, find the value of k.
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Step-by-Step Solution
Step 1: Apply Section Formula for x-coordinate
Let the point P(-1, k) divide the line segment joining A(−3,10) and B(6,−8) in the ratio m1:m2. We use the section formula for the x -coordinate to find this ratio. Here, x=−1, x1=−3, and x2=6.
Step 2: Calculate the ratio
Substitute the given values into the section formula for the x -coordinate and solve for the ratio m1:m2. This gives us the ratio in which the point divides the line segment.
Step 3: Apply Section Formula for y-coordinate
Now that we have the ratio m1:m2=2:7, we can use the section formula for the y -coordinate to find the value of k. Here, y=k, y1=10, and y2=−8.
Step 4: Calculate the value of k
Substitute the ratio m1=2, m2=7, and the y -coordinates into the section formula. Perform the arithmetic to find the value of k.