Chapter 37: Chapter 37

Find the equation of the perpendicular bisector of the line segment whose endpoints are \((-2,1)\) and \((3,-5)\)

Find the equation of the perpendicular bisector of that portion of the straight line \(5 \mathrm{x}+3 \mathrm{y}-15=0\) which is intercepted by the coordinate axes.

Find the point of intersection of two lines, \(4 \mathrm{x}+2 \mathrm{y}-1=0\), \(\mathrm{x}-2 \mathrm{y}-7=0\)

Let $\mathrm{A}(\mathrm{a}, \mathrm{c}), \mathrm{A}^{\prime}\left(\mathrm{a}, \mathrm{c}^{\prime}\right), \mathrm{B}\left(\mathrm{b}, \mathrm{d}^{\prime}\right)$ be four non-collinear points. Prove \(\underline{A B} \| \underline{A^{\prime} B^{\prime}}\) if and only if \(c-c^{\prime}=d-d^{\prime}\).

Given a line, \(\ell\), with the equation \(\mathrm{ax}+\mathrm{by}=\mathrm{c}\) and a point external to the line, \(P\), with the coordinates $\left(x_{1}, y_{1}\right)\(, show that the distance, \)\mathrm{d}$, between the point and the line is given by the formula $$ \left.\mathrm{d}=\mid \mathrm{ax}_{1}+\mathrm{by}_{1}-\mathrm{c} / \sqrt{(} \mathrm{a}^{2}+\mathrm{b}^{2}\right) \mid $$

Graph \(\\{(x, y): y=x+1\\}\)

Find (a) the x-intercept and (b) the y-intercept of the graph of the equation \(3 x-2 y=12\)

Draw the graph of \(\mathrm{x}+3 \mathrm{y}=6\)

Draw the graph of \(3 \mathrm{y}-2 \mathrm{x}=-6\), using its slope and \(\mathrm{y}\) intercept.

Find, graphically, the common solution for the system of equations: a) \(x+y=4\) b) \(\mathrm{y}=\mathrm{x}+2\)