Question

Point A is on x-axis point B is on y-axis and the point "P" lies on the line segment AB, such that P(4,5) and AP:PB = 5:3. find the coordinates of A and B​

Answer 1

Answer:

Hence, the coordinates of A are: $(\dfrac{32}{3},0)$

and that of B are: $(0,8)$

Step-by-step explanation:

As point A is on the x-axis hence the coordinates of point A are: (a,0)

and Point B lie on the y-axis hence the coordinates of Point B are: (0,b)

Point "P" lies on the line segment AB, such that P(4,5) and AP:PB = 5:3.

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We know that if any point C(c,c') divide the line segment A(a,a') and B(b,b') in the ratio m:n; then the coordinates of C is given by:

$c=\dfrac{m\times b+n\times a}{m+n}$ and $c'=\dfrac{m\times b'+n\times a'}{m+n}$ )

This means that:

$4=\dfrac{5\times 0+3\times a}{5+3}\\\\4=\dfrac{3a}{8}\\\\a=\dfrac{32}{3}$

and

$5=\dfrac{5\times b+3\times 0}{5+3}\\\\5=\dfrac{5b}{8}\\\\b=8$

Hence, the coordinates of A are: $(\dfrac{32}{3},0)$

and that of B are: $(0,8)$