Question

Demonstrate the translation of a line segment of 3 units to the left and 5 units down if the endpoints of the line segment are (-2, 7) and (0,3).

(-5, 7) and (-3, 3)
(1, 2) and (3, -2)
(-7, 4) and (-3 -2)
(-5, 2 and (-3, -2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct translation of the line segment would be:

Endpoint 1: (-2, 7)
After translating 3 units to the left and 5 units down:
New coordinate: (-2 - 3, 7 - 5)
= (-5, 2)

Endpoint 2: (0, 3)
After translating 3 units to the left and 5 units down:
New coordinate: (0 - 3, 3 - 5)
= (-3, -2)

Therefore, the translated endpoints of the line segment would be (-5, 2) and (-3, -2).

Answer 2

If a line signet with end points, 6, 3 and 6, 7 is translated 3 units up and 4 units to the right. How long is the line second after the translation?

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the length of the line segment after the translation, we can use the distance formula.

First, let's find the new coordinates of the endpoints after the translation:

Endpoint 1: (6, 3)
After translating 3 units up and 4 units to the right:
New coordinate: (6 + 4, 3 + 3)
= (10, 6)

Endpoint 2: (6, 7)
After translating 3 units up and 4 units to the right:
New coordinate: (6 + 4, 7 + 3)
= (10, 10)

Now, let's find the length of the line segment using the distance formula:

Length = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(10 - 10)^2 + (10 - 6)^2]
= √[0 + 16]
= √16
= 4

Therefore, the length of the line segment after the translation is 4 units.