Quiz about Unit 6 - Milestone Review

Question 1

The point $$\left(-4,-2\right)$$ lies on a circle. What is the length of the radius of this circle if the center is located at $$\left(-8,\ -10\right)$$ ?

Accepted Answer

$$\sqrt[]{80}$$

Answer

$$\sqrt[]{48}$$

Answer

$$\sqrt[]{108}$$

Answer

$$\sqrt[]{288}$$

Question 2

When proving that a quadrilateral is a parallelogram by using slopes, you must find:

Accepted Answer

both the lengths and slopes of all four sides.

Answer

the slopes of all four sides

Answer

the slopes of two opposite sides.

Answer

the lengths of all four sides.

Question 3

When proving that a triangle is a right triangle using coordinate geometry methods, you must:

Accepted Answer

both choices 1 and 2 may be used.

Answer

show that the slopes of two of the sides are negative reciprocals creating perpendicular lines and right angles.

Answer

show that the lengths of the sides satisfy the Pythagorean Theorem, thus creating a right angle.

Answer

neither choice 1 nor 2 may be used.

Question 4

A line passes through point $$A$$ at $$\left(2,\ 3\right)$$ and point $$B$$ at $$\left(4,\ 7\right)$$ . Which is the equation of $$\overline{BC}$$ if $$\overline{AB}\ \perp\overline{\ BC}$$ ?

Accepted Answer

$$y=-\frac{1}{2}x+9$$

Answer

$$y=-2x+5$$

Answer

$$y=-\frac{1}{2}x+5$$

Answer

$$y=\frac{1}{2}x+5$$

Question 5

Which line is parallel to the line described by $$2x+3y=6$$ ?

Accepted Answer

$$2x+3y=-6$$

Answer

$$3x+2y=6$$

Answer

$$3x-2y=-6$$

Answer

$$2x-3y=6$$

Question 6

Here are four linear equations. Which pair of lines are parallel?

Accepted Answer

II and IV

Answer

I and II

Answer

I and III

Answer

III and IV

Question 7

Here are four linear equations.

Which line is NOT parallel to the rest?

Accepted Answer

III

Answer

I

Answer

II

Answer

IV

Question 8

A student enters the following information into his/her calculator when attempting to find the slope between the points (6,7) and (-5,3). Which of the following statements is TRUE?

Accepted Answer

The slope is actually $$\frac{4}{11}$$

Answer

The student is correct, the slope is 11.5

Answer

The slope formula does not involve subtraction.

Answer

The slope is actually -11.5

Question 9

What is the distance between (7, -3) and (-5, 6)?

Accepted Answer

15

Answer

4

Answer

9

Answer

21

Question 10

What are the coordinates of the midpoints of $$\overline{BL}$$ with endpoints $$B\left(-7,\ -4\right)$$ and $$L\left(2,\ 3\right)$$ ?

Accepted Answer

$$\left(-2\frac{1}{2},\ -\frac{1}{2}\right)$$

Answer

$$\left(-3\frac{1}{2},\ -1\frac{1}{2}\right)$$

Answer

$$\left(-1\frac{1}{2},\ 0\right)$$

Answer

$$\left(-5,\ -1\right)$$

Question 11

Find the coordinates of $$P$$ such that $$P$$ divided the line segment from $$A\left(1,\ 3\right)$$ to $$B\left(8,\ 4\right)$$ into a 4 to 1 ratio.

Accepted Answer

$$\left(-4.6,\ 2.2\right)$$

Answer

$$\left(6.6,\ 3.8\right)$$

Answer

$$\left(7,\ 1\right)$$

Answer

$$\left(1.8,\ 8.6\right)$$

Question 12

Find the coordinates of the midpoints of $$\overline{MN}$$ with endpoints $$M\left(-3,\ 8\right)$$ and $$N\left(-7,\ 6\right)$$ .

Accepted Answer

$$\left(-5,\ 7\right)$$

Answer

$$\left(5,\ -7\right)$$

Answer

$$\left(2,\ 1\right)$$

Answer

$$\left(-2,\ -1\right)$$

Question 13

$$K$$ is the midpoint of $$\overline{PQ}$$ , $$P$$ has coordinates $$\left(-9,\ -4\right)$$ and $$K$$ has coordinates $$\left(-1,\ 6\right)$$ . What are the coordinates of $$Q$$ ?

Accepted Answer

$$\left(7,\ 16\right)$$

Answer

$$\left(-5,\ 1\right)$$

Answer

$$\left(5,\ 10\right)$$

Answer

$$\left(-11,\ 8\right)$$

Question 14

$$M$$ is the midpoint of $$\overline{RS}$$ , $$R$$ has coordinates $$\left(-12,\ 4\right)$$ and $$M$$ has coordinates $$\left(1,\ -2\right)$$ . What are the coordinates of $$S$$ ?

Accepted Answer

$$\left(14,\ -8\right)$$

Answer

$$\left(-5.5,\ -1\right)$$

Answer

$$\left(-11,\ 2\right)$$

Answer

$$\left(13,\ 6\right)$$

Question 15

What is the distance from $$V$$ to $$M$$ ?

Accepted Answer

17 cm

Answer

23 cm

Answer

120 cm

Answer

289 cm

Question 16

What is the distance from $$M\left(-1,\ 6\right)$$ and $$N\left(11.\ 1\right)$$ ?

Accepted Answer

$$13$$ units

Answer

$$12$$ units

Answer

$$\sqrt[]{149}$$ units

Answer

$$169$$ units

Question 17

What is the perimeter of the polygon formed by the points

$$P\left(-4,\ 1\right)$$ , $$Q\left(2,\ 4\right)$$ , $$R\left(4,\ 0\right)$$ , and $$S\left(-2,\ -3\right)$$ ?

Accepted Answer

$$10\sqrt[]{5}$$ units

Answer

$$18\ $$ units

Answer

$$9\sqrt[]{5}$$ units

Answer

$$20$$ units

Question 18

The area of a rectangular office is 288 square feet. One side of the office is 18 feet long. What is the perimeter of the office?

Accepted Answer

68 ft

Answer

34 ft

Answer

72 ft

Answer

88 ft

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