Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence, find m.
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Step-by-Step Solution
Step 1: Apply Section Formula for x-coordinate
We use the section formula to find the ratio in which point P divides the line segment AB. Let the ratio be k:1. The coordinates of point P are (x, y), and the coordinates of points A and B are (x1,y1) and (x2,y2) respectively. We substitute the given x -coordinates into the formula.
Step 2: Calculate the ratio k
Substitute the given x -coordinates: x=4, x1=2, and x2=6 into the section formula. Then, solve the equation for k. This gives us the ratio in which P divides AB.
Step 3: State the ratio
Since we found k=1, the ratio in which P divides the line segment AB is 1:1. This means P is the midpoint of AB.
Step 4: Apply Section Formula for y-coordinate
Now we use the section formula for the y -coordinate to find the value of m. We already know the ratio k=1, and the y -coordinates of A and B are y1=3 and y2=−3 respectively. The y -coordinate of P is m.
Step 5: Calculate m
Substitute k=1, y1=3, and y2=−3 into the section formula for the y -coordinate. Perform the arithmetic to find the value of m.