Unit 5 Assessment Review

Midpoint and Distance Formulas

How to find the exact middle of a segment and the distance between two points

​Distance Formula

​Distance Formula

1. Name your x and y values if on a coordinate plane​

2. You are going to subtract the x values.

3. ​You will then square, multiply the number it self.

4. ​Repeat Steps 1 and 2 with y value.

5. ​Add the 2 numbers together

6. ​Take square root.

   ​

Fill in the Blanks

Find the distance between

$\left(4,\ 9\right)\ and\ \left(7,\ 15\right)$  

Use calculator to estimate the answer, round to nearest tenths, first number after decimal

Fill in the Blanks

Distance betweeen 2 points.

​Midpoint Formula

​Midpoint Formula

1. ​You are going to add the x values together

1. ​Divide answer for Step 1 by 2.

2. ​Repeat steps 1 and 2 for the y values.

3. ​Write answer as an ordered pair (x, y)

Multiple Choice

Find the midpoint

$$\left(3,\ 7\right)\ \left(11,\ 19\right)$$  

What is the sum of x values?

• 3

• 8

• 14

• 33

Multiple Choice

Find the midpoint

$$\left(3,\ 7\right)\ \left(11,\ 19\right)$$  

What do you get when you divide the x value by 2?

• 28

• 7

• 14

• 64

Multiple Choice

Find the midpoint

$$\left(3,\ 7\right)\ \left(11,\ 19\right)$$  

What is the sum of y values?

• 26

• 12

• 8

• 56

Area of a Circle

Hint: Square the radius before multiplying by 3.14

Multiple Choice

Find the area of the circle with the given radius.

r = 6.4 in

• 40.96

• 403.8

• 128.6

Multiple Choice

Find the area of the circle with the given radius.

r = 9.4 ft

• 88.36

• 871.2

• 277.4

Arc Length and Sector Area

ARC LENGTH

Multiple Choice

In a​ circle, a 90° sector has area 64π in². What is the radius of the​ circle?

• 16 in

• 32 in

• 64 in

• 128 in

Multiple Choice

If the length of the 45° region of this circle is $$10\Pi$$   inches, what is the radius of the circle?

• 40 in.

• $$4\sqrt{5}$$  in.

• 10 in.

• 20 in.

Multiple Choice

Calculate the length of the bold arc.

• 49.7 ft

• 15.8 ft

• 24.9 ft

• 3.14 ft

Multiple Choice

Calculate the area of the sector.

• 4248 m²

• 7.9 m²

• 2827.4 m²

• 11.8 m²

Tangent Properties

Geometry Chapter 10

Tangent and Radius Property

If a tangent and a radius (or diameter) meet, they are PERPENDICULAR.

Multiple Choice

Find the length of the missing segment.

• 12

• 34

• 169

• 13

Two Tangents

If two tangents meet at the same exterior point, the segments are CONGRUENT.

Multiple Choice

How can we solve for x in this example?

• add both expressions together and subtract from 360

• set both expressions equal to each other

• use Pythagorean Theorem

• use magic

• combine like terms

Multiple Choice

#1 Line AB is tangent to circle C. Find the value of x.

• 98.18

• 117

• 153.3

• 108

Fill in the Blanks

#2 Find the value of x.

Fill in the Blanks

Find the value of x.

Fill in the Blanks

Find the value of x.

Fill in the Blanks

Fill in the Blanks

Find the value of x.

Fill in the Blanks

Find the value of x.

Multiple Choice

Circle E has congruent chords AB & CD.

If arc AB=92 degrees, then what is arc CD?

• 46

• 92

• 184

Multiple Choice

In circle E, chord AB=9.

Find CD.

• 3

• 4.5

• 9

• 18

Multiple Choice

In circle Z, arc WUX=160.

Find arc UX.

• 40

• 80

• 160

• 180

Multiple Choice

In circle A, chord BC=14.

Find BD.

• 2

• 7

• 14

• 21

Multiple Choice

Find x.

• 10

• 5

• 18

• 9

Multiple Choice

In circle R, chords MN=PO.

Find RS.

• 15

• 13

• 10

• 28

Multiple Choice

Use chords to solve for x

• x = 35^o

• x = 50^o

• x = 70^o

• x = 140^o

Central and Inscribed Angles Review

Multiple Choice

What is

$$measure\ of\ \angle EDF?$$  

• 120 degrees

• 180 degrees

• 60 degrees

• 360 degrees

Multiple Choice

$$What\ is\ measure\ of\ \angle XWE?$$  

• 180 degrees

• 56 degrees

• 112 degrees

• 360 degrees

Multiple Choice

Solve for the missing angle.

• 45^o
• 90^o
• 22.5^o
• 128^o

Multiple Choice

What is the measure of arc AD?

• 38
• 142
• 180
• 153

Parabolas

Equations and Parts

Multiple Choice

The vertex is halfway between the focus and directrix.

• True

• False

Steps on how to solve given the vertex and the focus:

​1. Determine what coordinates that has been changed.

​2. Once determined, choose the equation that corresponds to the changes.

​3. Solve for p and look for the focus part/formula.

​4. Substitute the value of p and the value of vertex in the given equation.

​Example:

​1. Write an equation of a parabola with vertex (-1,4) and focus (-1,2).

​Solution:

​4+p = 2

​p = 2-4

​p = -2

​

​y = 1/4p (x-h)²+k

​y = 1/4(-2) (x-(-1))²+4

​y = -1/8 (x+1)²+4

Multiple Choice

Write an equation of a parabola with a vertex of (-4, -1) and focus of (-4,6).

• $$y=\frac{1}{28}\left(x+4\right)^2-1$$  

• $$y=-\frac{1}{28}\left(x+4\right)^2+1$$  

• $$y=\frac{1}{20}\left(x-4\right)^2-1$$  

• $$y=-\frac{1}{20}\left(x-4\right)^2-1$$  

​Steps on how to solve given the vertex and the directrix:

​1. Determine what letter has been given.

​2. Once determined, choose the equation that corresponds to the letter.

​3. Solve for p and look for the directrix part/formula.

​4. Substitute the value of p and the value of vertex in the given equation.

​Example:

​Write an equation of a parabola with vertex (2, -4) and directrix of y = -6.

​Solution:

​

​

​

​                     -6 = -4 - p

​                   -6 + 4 = - p

​                          -2 = -p

​                             2 = p

Multiple Choice

Write an equation of a parabola with vertex (-4, -1) and directrix of y = -8.

• $$x=-\frac{1}{28}\left(y+4\right)^2-1$$  

• $$y=-\frac{1}{28}\left(x+4\right)^2-1$$  

• $$x=\frac{1}{28}\left(y+4\right)^2-1$$  

• $$y=\frac{1}{28}\left(x+4\right)^2-1$$