1) Two lines \(y - ax = 2\) and \(x+23y = 138\) are perpendicular to each other. What is the value of \(a\)?
2) \(\overline{RT}\) has the equation \(y = 2x + 3\). Find equations of the line segments forming the other three sides of
the rectangle.
2) \(\overline{RT}\) has the equation \(y = 2x + 3\). Find equations of the line segments forming the other three sides of
the rectangle.
3) A quadrilateral has the following coordinates: \(A(4, 5), B(8, 2), C(13, 10),\) and \(D(x, y)\). Find \(x\) and \(y\) such that
\(\overline{AB}\parallel\overline{CD}\) and \(\overline{BC}\parallel\overline{AD}\).
4) Given: \(y = \frac{1}{2}x + 6\) \(\frac{2}{3}x - \frac{1}{3}y = 1\) \(y - 5 = -2(x - 3)\)
\(-x + 2y = 12\) \(4x + 2y - 6 = 0\) \(y = 2x + 6\)
If two equations are selected at random, what is the probability that the lines would be:
a) parallel? b) perpendicular? c) neither?
Solution Bank
\(\overline{AB}\parallel\overline{CD}\) and \(\overline{BC}\parallel\overline{AD}\).
4) Given: \(y = \frac{1}{2}x + 6\) \(\frac{2}{3}x - \frac{1}{3}y = 1\) \(y - 5 = -2(x - 3)\)
\(-x + 2y = 12\) \(4x + 2y - 6 = 0\) \(y = 2x + 6\)
If two equations are selected at random, what is the probability that the lines would be:
a) parallel? b) perpendicular? c) neither?
Solution Bank