Question

Point a is on x axis,point b on y axis and point p lies on line segment ab such that p = (4,5) and ap:bp =5:3. Find coordinates of point a and b

Answer 1

Answer:

Please look at the figure in the attachment drawn according to the question.

We need to find the coordinates of Point a and b

So, Using section formula:

$(x,y)=\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2}$

Here,$m_1=3,m_2=5,x_1=a,y_1=0,x_2=0,y_2=b.x=4,y=5$

On substituting the values in the above section formula we get:

$(4,5)=\frac{3(0)+5(a}{3+5},\frac{3(b)+5(0)}{3+5}$

Equating coordinates of x with x and y with y.

$(4,5)=\frac{5a}{8},\frac{3b}{8}$

$4=\frac{5a}{8},5=\frac{3b}{8}$

$a=\frac{32}{5},b=\frac{40}{3}$

So, the coordinates will be $(\frac{32}{5},0)\text{and}(0,\frac{40}{3})$