Find the coordinates of the point dividing the line segment joining A(3, 5) and B(9, 11) internally in the ratio 2 : 1.
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Step-by-Step Solution
Step 1: Identify Given Information
First, we identify the given coordinates of the two points, A and B, and the ratio in which the line segment AB is divided. Let the coordinates of point A be (x1,y1) and point B be (x2,y2). The given ratio is m1:m2=2:1.
Step 2: Recall 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 Formula
Now, we substitute the values of x1,y1,x2,y2,m1, and m2 into the section formula. This will give us the expressions for the x and y coordinates of the dividing point.
Step 4: Calculate Coordinates
Finally, we perform the arithmetic operations to calculate the exact values of x and y. This gives us the coordinates of the point that divides the line segment.