coordinate plane with trapezoids TRAP and T prime R prime A prime P prime and points W, X, Y, and Z with points located at T 1 comma 1, R 2 comma 3, A 4 comma 3, P 5 comma 1, T prime 2 comma one half, R prime 2 and one half comma one and one half, A prime 3 and one half comma one and one half, P prime 4 comma one half, W 2 and one half comma negative one and one half, X 0 comma 3, Y 5 comma negative 1, and Z 6 comma 1
Trapezoid TRAP was dilated by a scale factor of one half to create trapezoid T′R′A′P′.
Which point is the center of dilation?
W
X
Y
Z
Question 2(Multiple Choice Worth 1 points)
(03.01 MC)
coordinate plane with points at A 0 comma 2 and B 2 comma 0 intersected by line f
Dilate line f by a scale factor of 3 with the center of dilation at the origin to create line f′. Where are points A′ and B′ located after dilation, and how are lines f and f′ related?
The locations of A′ and B′ are A′ (0, 2) and B′ (6, 0); lines f and f′ intersect at point A.
The locations of A′ and B′ are A′ (0, 6) and B′ (2, 0); lines f and f′ intersect at point B.
The locations of A′ and B′ are A′ (0, 2) and B′ (2, 0); lines f and f′ are the same line.
The locations of A′ and B′ are A′ (0, 6) and B′ (6, 0); lines f and f′ are parallel.
Question 3(Multiple Choice Worth 1 points)
(03.01 MC)
Coordinate plane with quadrilaterals EFGH and E prime F prime G prime H prime at E 0 comma 1, F 1 comma 1, G 2 comma 0, H 0 comma 0, E prime negative 1 comma 2, F prime 1 comma 2, G prime 3 comma 0, and H prime negative 1 comma 0. F and H are connected by a segment, and F prime and H prime are also connected by a segment.
Quadrilateral EFGH was dilated by a scale factor of 2 from the center (1, 0) to create E′F′G′H′.
Which characteristic of dilations compares segment E′F′ to segment EF?
A segment that passes through the center of dilation in the pre-image continues to pass through the center of dilation in the image.
A segment in the image has the same length as its corresponding segment in the pre-image.
A segment that passes through the center of dilation in the pre-image does not pass through the center of dilation in the image.
A segment in the image is proportionally longer or shorter than its corresponding segment in the pre-image.
Question 4(Multiple Choice Worth 1 points)
(03.01 MC)
Triangle ABC is translated by the rule (x + 1, y + 1) and then dilated by a scale factor of 2 centered at the origin. Which statement describes the properties of triangles ABC and A″B″C″ after the transformations?
∠C and ∠C″ are congruent after both the translation and the dilation.
∠C and ∠C″ are congruent after the dilation, but not after the translation.
segment AC and segment A double prime C double prime are congruent after both the translation and the dilation.
segment AC and segment A double prime C double prime are congruent after the dilation, but not after the translation.
Question 5(Multiple Choice Worth 1 points)
(03.01 MC)
Coordinate plane with triangle EFG with E at 0 comma 5, F at 1 comma 1, and G at negative 2 comma 1. Point H at 1 comma 1 is on segment GF, and points E and H are connected with a segment.
Triangle EFG is dilated by a scale factor of 3 centered at (0, 1) to create triangle E′F′G′. Which statement is true about the dilation?
segment EH and segment E prime H prime both pass through the center of dilation.
The slope of segment EF is the same as the slope of segment E prime H prime.
segment E prime G prime will overlap segment EG.
segment EH ≅ segment E prime H prime.
Question 6(Multiple Choice Worth 1 points)
(03.01 MC)
Hexagon IJKLMN is shown on the coordinate plane below:
hexagon IJKLMN on a coordinate plane with ordered pairs at I negative two, six, at J four, four, at K six, negative one, at L negative one, two, at M negative four, negative four, and at N negative six, two
If hexagon IJKLMN is dilated by a scale factor of two fifths from the origin to create hexagon I′J′K′L′M′N′, what is the ordered pair of point N′?
Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was three fourths the size of the brand name. If the generic television set is 12 inches by 24 inches, what are the dimensions of the brand name television?
18 inches by 36 inches
6 inches by 12 inches
16 inches by 32 inches
9 inches by 18 inches
Question 8(Multiple Choice Worth 1 points)
(03.01 MC)
Pentagon OPQRS is shown on the coordinate plane below:
Pentagon OPQRS on a coordinate plane with ordered pairs at O negative 1, 2, at P negative 5, 3, at Q negative 3, negative 2, at R 2, 1, and at S 2, 5.
If pentagon OPQRS is dilated by a scale factor of seven over four from the origin to create O′P′Q′R′S′, what is the ordered pair of point P′?
segment M prime N prime has endpoints located at M′ (−2, 0) and N′ (2, 0). It was dilated at a scale factor of 2 from center (2, 0). Which statement describes the pre-image?
segment MN is located at M (0, 0) and N (2, 0) and is half the length of segment M prime N prime.
segment MN is located at M (0, 0) and N (2, 0) and is twice the length of segment M prime N prime.
segment MN is located at M (0, 0) and N (4, 0) and is half the length of segment M prime N prime.
segment MN is located at M′ (0, 0) and N (4, 0) and is twice the length of segment M prime N prime.
Question 10(Multiple Choice Worth 1 points)
(03.01 LC)
coordinate plane with segment AB located at A 0 comma 2 and B 2 comma 3
segment AB is dilated from the origin to create segment A prime B prime at A′ (0, 6) and B′ (6, 9). What scale factor was segment AB dilated by?
one half
2
3
4
1 answer
Here are the answers for each of your multiple-choice questions:
Question 1: Answer: Z (the center of dilation is determined by the relationship between original and dilated points).
Question 2: Answer: The locations of A′ and B′ are A′ (0, 6) and B′ (6, 0); lines f and f′ are parallel.
Question 3: Answer: A segment that passes through the center of dilation in the pre-image continues to pass through the center of dilation in the image.
Question 4: Answer: ∠C and ∠C″ are congruent after both the translation and the dilation.
Question 5: Answer: segment EH and segment E prime H prime both pass through the center of dilation.
Question 6: Answer: (−0.4, 0.8) (the calculation would be: N (−6, 2) * (2/5) = (−0.4, 0.8)).
Question 7: Answer: 18 inches by 36 inches (18 and 36 are 3/4 of the dimensions of 12 and 24).
