Find the coordinates of the point which divides the line segment joining (4, -3) and (8, 5) in the ratio 3:1 internally.
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Step-by-Step Solution
Step 1: Identify given values
We are given two points, (x1,y1)=(4,−3) and (x2,y2)=(8,5). We are also given the ratio in which the line segment joining these points is divided, which is m1:m2=3:1.
Step 2: Recall the Section Formula
To find the coordinates of a point that divides a line segment internally in a given ratio, we use the section formula. This formula helps us calculate the x and y coordinates of the dividing point.
Step 3: Substitute values into the formula
Now, we substitute the identified values of x1,y1,x2,y2,m1, and m2 into the section formula to find the x and y coordinates of the point P.
Step 4: Calculate the x-coordinate
First, we calculate the x -coordinate. We perform the multiplication and addition in the numerator, then divide by the sum of the ratios.
Step 5: Calculate the y-coordinate
Next, we calculate the y -coordinate. Similar to the x -coordinate, we perform the operations in the numerator and then divide by the sum of the ratios.
Step 6: State the coordinates of the point
Combining the calculated x and y coordinates, we get the coordinates of the point that divides the line segment in the given ratio.