Question

calculate at what distance from the origin ,the graphic of the equation X/2+y/3 =1 intersects the x axis and they y axis...​

Answer 1

Answer:

x-axis :- at a distance of 2 units.

y-axis :- at a distance of 3 units.

Concepts

• The ordinate(y co-ordinate) of any point lying on the x-axis is zero.

• Similarly,the absicca (x co-ordinate) of any point lying on the y-axis is zero.

• The distance of (a,0) and (0,a) from origin is a units.

Calculations

Given,equation of the line :- $\dfrac{x}{2}\:+\: \dfrac{y}{3}\:=\:1$

To check for point where it cuts x-axis

Put y = 0

:- $\dfrac{x}{2}\:+\: \dfrac{0}{3}\:=\:1$

$\implies \: \dfrac{x}{2}\:=\:1$

$\implies \: x\:=\:2$

• Hence,the point is (2,0). Its distance from origin is 2 units.

To check for point where it cuts y-axis

Put y = 0

:- $\dfrac{0}{2}\:+\: \dfrac{y}{3}\:=\:1$

$\implies \: \dfrac{y}{3}\:=\:1$

$\implies \: y\:=\:3$

• Hence,the point is (0,3). Its distance from origin is 3 units.