Question

Problem 21) Use the midpoint formula to calculate the midpoint of this line segment.



(1 point)
Responses

Midpoint = (1,2)
Midpoint = (1,2)

Midpoint = (6,5)
Midpoint = (6,5)

Midpoint = (3,2)
Midpoint = (3,2)

Midpoint = (9,1)
Midpoint = (9,1)
Question 22
Problem 22) Find the coordinate of point M such that the partition has a ratio of AM:MB = 2:3.



(1 point)
Responses

M = (-5,-1)
M = (-5,-1)

M = (1,-1)
M = (1,-1)

M = (-2,-2)
M = (-2,-2)

M = (-2,-1)
M = (-2,-1)
Question 23
Problem 23) What is the scale factor of dilation for the triangles below?



(1 point)
Responses

k = 1
k = 1

k = 2
k = 2

k = 5
k = 5

k = 7
k = 7
Question 24
Problem 24) Which type of transformation is also known as a "nonrigid transformation"?(1 point)
Responses

Translation
Translation

Reflection
Reflection

Rotation
Rotation

Dilation
Dilation
Question 25
Problem 25) What theorem could we use to prove that triangle △MNQ is similar to triangle △PNO, based on the information below?



(1 point)
Responses

SSS~
SSS~

SAS~
SAS~

AA~
AA~

Pythagorean Theorem
Pythagorean Theorem
Question 26
Problem 26) Find the value of x with the Triangle Midsegment Theorem.



(1 point)
Responses

x = 13
x = 13

x = 11
x = 11

x = 9
x = 9

x = 5
x = 5
Question 27
Problem 27) The triangles below are proportional (related by a scale factor of dilation). Use this information to find the value of x.



(1 point)
Responses

x = 5
x = 5

x = 3
x = 3

x = 12
x = 12

x = 20
x = 20
Question 28
Problem 28) I've drawn a rectangle with side lengths of 4in and 9in (shown below). Next, I'll dilate this figure by a factor of 2. What will be the area of the new rectangle?



(1 point)
Responses

Area = 96
Area = 96

Area = 45
Area = 45

Area = 67
Area = 67

Area = 144
Area = 144
Question 29
Problem 29) Here is a picture of two squares that are related by a scale factor of dilation, k. Based on the areas of the squares below, what is the scale factor of dilation? Hint: make sure you calculate the side lengths first!!



(1 point)
Responses

k = 1
k = 1

k = 2
k = 2

k = 3
k = 3

k = 4
k = 4
Question 30
Problem 30) Use the geometric mean to calculate the value of x.



(1 point)
Responses

x = 2
x = 2

x = 3
x = 3

x = 4
x = 4

x = 5
x = 5
Question 31
Problem 31) Use the geometric mean to calculate the value of the altitude, x.



(1 point)
Responses

x = 2
x = 2

x = 3
x = 3

x = 6
x = 6

x = 9
x = 9
Question 32
Bonus Question) What is your favorite theorem that you learned this semester in geometry? Note: all options are marked correct, so you will earn credit regardless of the answer that you choose.(1 point)
Responses

CPCTC Theorem
CPCTC Theorem

Triangle Sum Theorem
Triangle Sum Theorem

Side-Angle-Side Theorem (SAS)
Side-Angle-Side Theorem (SAS)

Vertical Angles Theorem

Answer 1

I can help, but I’m missing the diagrams and coordinates for most of these questions (they’re required to compute exact answers). Please upload the images or paste the coordinates/measures shown for problems 21–23, 25–27, 29–31. Meanwhile I’ll give short formulas and steps so you can quickly get each answer once you provide the missing info.

Quick definite answers I can give now:
- Q24: Dilation (a dilation is a “nonrigid transformation”).
- Q28: Area after dilation by 2 of a 4 in × 9 in rectangle: new sides 8 and 18, area = 8 × 18 = 144.
- Q32 (bonus): Any choice is correct (you’ll get credit). Pick whichever you like.

How to solve the other problems (formulas and steps)

Q21 — Midpoint formula
- If endpoints are A(x1,y1) and B(x2,y2), midpoint M = ((x1 + x2)/2, (y1 + y2)/2).
- Plug the given coordinates into that formula and choose the matching option.

Q22 — Partition point M so AM:MB = 2:3
- If A(xA,yA) and B(xB,yB), fraction along from A to B = AM/AB = 2/(2+3) = 2/5.
- M = ( xA + (2/5)(xB − xA) , yA + (2/5)(yB − yA) ).
- Equivalent weighted formula: M = ( (3·xA + 2·xB)/5 , (3·yA + 2·yB)/5 ).
- Plug in A and B coordinates to pick the option.

Q23 — Scale factor of dilation between two triangles
- k = (corresponding side length of image) / (corresponding side length of preimage).
- Identify one pair of corresponding sides, compute the ratio, then pick the answer.

Q25 — Which similarity theorem?
- If two pairs of corresponding angles are equal (or two angles in each triangle), use AA~.
- If two sides are proportional and included angles equal, use SAS~.
- If three sides are proportional, use SSS~.
- Based on typical problems where you’re given angle information, AA~ is most common. If you can upload the figure I’ll confirm.

Q26 — Triangle midsegment theorem
- A midsegment is parallel to a side and equals half its length.
- If a midsegment or half-length relation is given, set up equation (midsegment = 1/2 × base) and solve for x.

Q27 — Proportional triangles (scale factor k)
- Find k by dividing a known corresponding side length in one triangle by the matching side length in the other.
- Then solve for x using x = (corresponding side in one triangle) / k (or multiply if appropriate).

Q29 — Scale factor for squares from areas
- If areas are A1 and A2, side lengths are s1 = sqrt(A1), s2 = sqrt(A2).
- k = s2 / s1 = sqrt(A2 / A1).
- Compute and pick the matching option.

Q30 — Geometric mean: x = sqrt(a · b)
- If asked for x as the geometric mean of two numbers a and b, compute x = sqrt(a × b).

Q31 — Geometric mean altitude in a right triangle
- If altitude to the hypotenuse splits it into segments p and q, altitude x = sqrt(p · q).
- If a leg a is adjacent to projection p on hypotenuse, leg a = sqrt(hypotenuse · p). Use whichever relation matches the diagram.

If you upload each problem’s diagram or the numeric values shown, I’ll compute and pick the exact multiple-choice answers for you.