Question

The point p(5,-2) divides the segment joining the points (x,0) and (0,y) in the ratio 2:5. what is the value of x and y?

Answer 1

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Answer 2

Answer:

The value of x is 7 and the value of y is -7

Step-by-step explanation:

Given : The point p(5,-2) divides the segment joining the points (x,0) and (0,y) in the ratio 2:5.

To Find: what is the value of x and y?

Solution :

We will use section formula :

$(x,y) =(\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n})$

P = (x,y)=(5,-2)

$(x_1,y_1)=(x,0)$

$(x_2,y_2)=(0,y)$

m:n= 2:5

$(5,-2) =(\frac{2\times 0 +5x }{2+5} ,\frac{2y+5\times 0}{2+5})$

$(5,-2) =(\frac{5x }{7} ,\frac{2y}{7})$

$\Rightarrow 5= \frac{5x}{7}$

$\Rightarrow 35= 5x$

$\Rightarrow \frac{35}{5}= x$

$\Rightarrow 7= x$

$\Rightarrow -2= \frac{2y}{7}$

$\Rightarrow -14= 2y$

$\Rightarrow \frac{-14}{2}= y$

$\Rightarrow -7= y$

Hence the value of x is 7 and the value of y is -7