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Question

Find the coordinates of the points at which line joining (2,3)and (3,2) meet the x-axis and y-axis respectively


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Solution

Find the equation of the line joining the given points and thus find its intercepts

Let (2,3)=x1,y1 and (3,2)=x2,y2

Using two point form of equation of a line

y-y1y2-y1=x-x1x2-x1

y-32-3=x-23-2

-y-3=x-2

x+y-5=0 ...(i)

x+y-5=0 is the equation of the line joining (2,3) and (3,2)

Now, we write this equation in double intercept form

xa+yb=1 where a is the x-intercept and b is the y-intercept

x+y=5 …[From(i)]

Dividing by 5 throughout the equation we get

x+y5=1

x5+y5=1

Hence, x-intercept=a=5

y-intercept=b=5

Hence the co-ordinates of the points where the line intersects the axes are

(x,0)=(5,0)(y,0)=(0,5)

Hence, the line joining (2,3)and (3,2) cuts the x-axis at 5,0 and the y-axis at 0,5 respectively.


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