Find the coordinates of the point which divides the line segment joining the points (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, P1(4,−3) and P2(8,5), which define the line segment. We are also given the ratio m:n=3:1 in which the point divides the segment internally. Here, m=3 and n=1.
Step 2: Apply 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 the values
Now, we substitute the identified values into the section formula. For the x -coordinate, we use m=3, x2=8, n=1, and x1=4. For the y -coordinate, we use m=3, y2=5, n=1, and y1=−3.
Step 4: Calculate the coordinates
Perform the arithmetic operations to find the values of x and y. First, calculate the numerators and denominators, then divide to get the final coordinates.
Step 5: State the final coordinates
The coordinates of the point that divides the line segment joining (4,−3) and (8,5) in the ratio 3:1 internally are (7,3).