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

​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

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

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.

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

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

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

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