Question

Select the coordinates A′

and B′
after dilation of the line segment AB
with a scale factor of 2, centered at the origin where the endpoints are A(3,7)
and B(4,9)
.(1 point)
Responses

A′(32,72)
and B′(2,92)
upper A prime left parenthesis Start Fraction 3 over 2 End Fraction comma Start Fraction 7 over 2 End Fraction right parenthesis and upper B prime left parenthesis 2 comma Start Fraction 9 over 2 End Fraction right parenthesis

A′(6,14)
and B′(8,18)
upper A prime left parenthesis 6 comma 14 right parenthesis and upper B prime left parenthesis 8 comma 18 right parenthesis

A′(−6,3)
and B′(8,18)
upper A prime left parenthesis negative 6 comma 3 right parenthesis and upper B prime left parenthesis 8 comma 18 right parenthesis

A′(6,14)
and B′(−4,3)
upper A prime left parenthesis 6 comma 14 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct answer is:

A′(6,14)
and B′(8,18)

Answer 2

Dilations & Lines Quick Check

2 of 52 of 5 Items
Question
Line AB
contains point A(−4, 1)
and point B (−1, 3)
. Find the coordinates of A′
and B′
after a dilation with a scale factor of 2 with a center point of dilation at the origin.(1 point)
Responses

A′ (−5, −2)
and B′ (−2, 6)
upper A prime left parenthesis negative 5 comma negative 2 right parenthesis and upper B prime left parenthesis negative 2 comma 6 right parenthesis

A′ (8, −2)
and B′ (2, −6)
upper A prime left parenthesis 8 comma negative 2 right parenthesis and upper B prime left parenthesis 2 comma negative 6 right parenthesis

A′ (−8, 2)
and B′ (−2, 6)
upper a prime left parenthesis negative 8 comma 2 right parenthesis and upper b prime left parenthesis negative 2 comma 6 right parenthesis

A′ (−8, 2)
and B′ (2, −6)

Answer 3

[AI-generated answer — Bot GPT 3.5]

The correct answer is:

A′ (−8, 2)
and B′ (−2, 6)

Answer 4

Line AB

contains point A(1, 2)
and point B (−2, −1)
. Find the coordinates of A′
and B′
after a dilation with a scale factor of 5 with a center point of dilation at the origin.(1 point)
Responses

A′ (5, 10)
and B′ (10, 5)
upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis 10 comma 5 right parenthesis

A′ (5, 10)
and B′ (−2, −1)
upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis negative 2 comma negative 1 right parenthesis

A′ (1, 2)
and B′ (−10, −5)
upper A prime left parenthesis 1 comma 2 right parenthesis and upper B prime left parenthesis negative 10 comma negative 5 right parenthesis

A′ (5, 10)
and B′ (−10, −5)

Answer 5

[AI-generated answer — Bot GPT 3.5]

The correct answer is:

A′ (5, 10)
and B′ (−10, −5)

Answer 6

[AI-generated answer — Step-by-Step Bot]

To find the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 2, centered at the origin, we multiply the x and y coordinates of A and B by the scale factor.

For A(3, 7):
A′ = (2 * 3, 2 * 7) = (6, 14)

For B(4, 9):
B′ = (2 * 4, 2 * 9) = (8, 18)

Therefore, the correct answer is:

A′(6, 14) and B′(8, 18)

Answer 7

[AI-generated answer — Explain Bot]

To find the coordinates of A′ and B′ after dilation of the line segment AB with a scale factor of 2 centered at the origin, we need to multiply the x-coordinate and y-coordinate of each point by the scale factor.

The original coordinates of point A are (3, 7), and the scale factor is 2. Therefore, the coordinates of A′ can be found by multiplying each coordinate by 2:
x-coordinate of A′ = 3 * 2 = 6
y-coordinate of A′ = 7 * 2 = 14

So, A′ is located at (6, 14).

Similarly, for point B with coordinates (4, 9), the dilation process is also applied:
x-coordinate of B′ = 4 * 2 = 8
y-coordinate of B′ = 9 * 2 = 18

Thus, B′ is located at (8, 18).

Therefore, the correct answer is:
A′(6,14) and B′(8,18)