Analytical Geometry

Question

I have Problem in Analytical Geometry Question: The Portion of a Straight line between the axes is bisected at the point (-3,2) Find its Equation

My Try I used Equation formula $$(y-y_1)=m(x-x_1)$$ but it requires Slope

Answer 1

Let $a$ & $b$ be the x-intercept & y-intercept respectively then the straight line will intersect the axes at the points $(a, 0)$ & $(0, b)$ respectively then the mid-point $(-3, 2)$ of the intersected portion of the line between the coordinate axes is given as $$(-3, 2)\equiv \left(\frac{a+0}{2}, \frac{0+b}{2}\right)$$ $$(-3, 2)\equiv \left(\frac{a}{2}, \frac{b}{2}\right)$$ Hence, by comparing the coordinates we get $$a=2(-3)=-6, b=2(2)=4$$ Then the equation of the line: using intercept formula of the line $$\frac{x}{a}+\frac{y}{b}=1$$ $$\frac{x}{-6}+\frac{y}{4}=1$$

$$\color{red }{2x-3y+12=0}$$