Find the coordinates of the point that divides the line segment joining P(1, 2) and Q(7, 8) internally in the ratio 1 : 2.
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Step-by-Step Solution
Step 1: Identify given values
We are given two points, P and Q, and the ratio in which a point divides the line segment PQ internally. Let the coordinates of P be (x1,y1) and Q be (x2,y2). The given ratio is m1:m2.
Step 2: Recall the Section Formula
To find the coordinates of a point R(x, y) that divides the line segment joining two points (x1,y1) and (x2,y2) internally in the ratio m1:m2, we use the section formula.
Step 3: Substitute the 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 R.
Step 4: Calculate the coordinates
Perform the arithmetic operations to simplify the expressions for x and y. This will give us the final coordinates of the point R.