The point P(4,5) divides AB internally in the ratio 1:1, where A(2,3) and B(x,y). What are the coordinates (x,y)?
(6,7)
Dividing AB in the ratio 1:1 means P is the midpoint of AB.
Midpoint formula: \(P = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)\)
For the x-coordinate: \(\frac{2 + x}{2} = 4 \Rightarrow 2 + x = 8 \Rightarrow x = 6\)
For the y-coordinate: \(\frac{3 + y}{2} = 5 \Rightarrow 3 + y = 10 \Rightarrow y = 7\)
So B = (6,7).
Hence, the answer is (6,7).
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In which ratio the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3)?
In which quadrant both abscissa and ordinate are negative?
Find the slope of the line joining the points (3, -4) and (5, 2).
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