The coordinate point P is at (6, 8) given AB with A(3,-1) and B(8, 14), if p lies on AB such that the ratio of AP to PB is 2:3 is (6, 8)
Midpoint is the point that divides a line into two equal parts.
The formula for calculating the midpoint of a line divided within the ratio a:b is expressed as:
[tex]M(X, Y)=(\frac{ax_1+bx_2}{a+b}, \frac{ay_1+by_2}{a+b} )[/tex]
Given the coordinate point A(3,-1) and B(8, 14) and the ratio 2:3
Get the X coordinate of point P
[tex]X = \frac{2(3)+3(8)}{2+3}\\X=\frac{6+24}{5} \\X = \frac{30}{5}\\X=6[/tex]
Get the Y coordinate of point P
[tex]Y = \frac{2(-1)+3(14)}{2+3}\\Y=\frac{-2+42}{5} \\Y = \frac{40}{5}\\Y=8[/tex]
hence the coordinate point P is at (6, 8)
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