Lines, Slopes, and Perpendicularity: Practice Level 1 | Geometry

Level 1 · Foundational 0 / 12 answered

Question 1 of 12

1

One slope triangle on a nonvertical line has rise 2 and run 5. Another has rise 6 and run 15. Which explanation establishes that the slopes agree?

Answer choices for question 1 A All right triangles are congruent B The triangles are similar by AA, so matching leg ratios agree C The hypotenuses must have the same length D A line must have positive slope
2

A nonvertical line through $(-2,7)$ has slope $-3/5$ . Which equation describes it?

Answer choices for question 2 A $y+7=-\frac35(x+2)$ B $y-7=\frac35(x+2)$ C $y-7=-\frac53(x+2)$ D $y-7=-\frac35(x+2)$
3

Compare the two equations.
$\begin{aligned}y&=\frac37x+2,\\7y&=3x+14.\end{aligned}$
What is their relationship?

Answer choices for question 3 A They describe the same line B Distinct parallel lines C Perpendicular lines D Lines with different slopes
4

The equations
$x-5=0$
and
$2x=14$
describe which relationship?

Answer choices for question 4 A The same vertical line B Perpendicular lines C Distinct parallel vertical lines D Two lines of slope zero
5

A right triangle along a line has run 5 right and rise 2 up. What is the slope of its image after a counterclockwise quarter-turn?

Answer choices for question 5 A $\frac52$ B $-\frac52$ C $-\frac25$ D $\frac25$
6

Two slanted lines have slopes $-4/7$ and $7/4$ . Which calculation establishes their perpendicularity?

Answer choices for question 6 A $(-\frac47)(\frac74)=-1$ B $-\frac47+\frac74=\frac{33}{28}$ C $(-\frac47)(\frac74)=1$ D $-\frac47=\frac74$
7

Through $P=(-6,3)$ , which line is perpendicular to the horizontal line $y=-8$ ?

Answer choices for question 7 A $y=3$ B $x=3$ C $y=-6$ D $x=-6$
8

Find the perpendicular bisector of a segment with endpoints $(-7,-2)$ and $(3,-2)$ .

Answer choices for question 8 A $y=-2$ B $x=3$ C $x=-2$ D $y=2$
9

Triangle $ABC$ has vertices
$\begin{aligned}A&=(-1,5),\\B&=(2,-5),\\C&=(8,3).\end{aligned}$
Which is its median line from $A$ ?

Answer choices for question 9 A $y=x+6$ B $y=-\frac34x+\frac{17}4$ C $y=-x+4$ D $x=5$
10

In a triangle, side $BC$ lies on the vertical line $x=4$ , and $A=(-2,6)$ . What is the altitude line from $A$ ?

Answer choices for question 10 A $x=-2$ B $y=6$ C $y=4$ D $x=6$
11

Find the intersection of the perpendicular bisector $x=-3$ and the median line $y=2x+8$ .

Answer choices for question 11 A $(2,-3)$ B $(-3,8)$ C $(0,8)$ D $(-3,2)$
12

Two nonvertical line equations have the same slope and contain the same point. Which conclusion is justified?

Answer choices for question 12 A They coincide B They are distinct parallels C They are perpendicular D They have no common points