The coordinates of the end points A and B of line segment AB are given by (2,3) and (7,11). If P and Q are points on AB such that AP=PQ=QB, what is the sum of the x-coordinates of the points P and Q?
Question
The coordinates of the end points A and B of line segment AB are given by (2,3) and (7,11). If P and Q are points on AB such that AP=PQ=QB, what is the sum of the x-coordinates of the points P and Q?
Solution
First, we need to understand that AP=PQ=QB means that the line segment AB is divided into three equal parts by points P and Q.
The total distance of the x-coordinates from A to B is 7 - 2 = 5. Since this is divided into three equal parts, each part is 5/3.
So, the x-coordinate of point P (which is 5/3 units from point A) would be 2 + 5/3 = 2 + 1.67 = 3.67 (rounded to two decimal places).
Similarly, the x-coordinate of point Q (which is 25/3 units from point A) would be 2 + 2(5/3) = 2 + 3.33 = 5.33 (rounded to two decimal places).
The sum of the x-coordinates of points P and Q is therefore 3.67 + 5.33 = 9.00.
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