Parallel and Perpendicular Lines: math test, Grade 10 – download the PDF

1 Angles and algebra / 4 pts

Parallel lines \(a\) and \(b\) are cut by a transversal. Two alternate interior angles measure \((7x - 4)^\circ\) and \((5x + 16)^\circ\).

1. Write and solve an equation for \(x\). (2 points)
2. Find the measure of the angles. (1 point)
3. Find the measure of a same-side interior angle of one of them. (1 point)

2 Prove parallel / 3 pts

A transversal crosses lines \(p\) and \(q\). Two same-side interior angles measure \(118^\circ\) and \(62^\circ\). (a) Are \(p\) and \(q\) parallel? Justify. (b) If the angles measured \(118^\circ\) and \(64^\circ\) instead, what would you conclude?

3 Slopes of three lines / 4 pts

Line \(\ell_1\) passes through \((-3, 4)\) and \((1, -2)\). Line \(\ell_2\) passes through \((0, 1)\) and \((3, 3)\). Line \(\ell_3\) passes through \((-1, 5)\) and \((3, -1)\). Find the three slopes (3 points) and name the relation between \(\ell_1\) and \(\ell_2\), and between \(\ell_1\) and \(\ell_3\) (1 point).

4 Writing equations / 4 pts

Line \(m\) is \(y = -\dfrac{3}{4}x + 2\). Write an equation of (a) the line through \((8, -1)\) parallel to \(m\) (2 points), and (b) the line through \((8, -1)\) perpendicular to \(m\) (2 points).

5 Distance to a line / 3 pts

Find the distance from the point \(P(1, 2)\) to the line \(3x + 4y + 5 = 0\). Show your work.

6 Perpendicular bisector / 2 pts

Find the equation of the perpendicular bisector of the segment joining \(A(-1, 0)\) and \(B(5, 4)\).