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)

Question

and (0, 3)
.(1 point)
Responses

(−5, 2)
and (−3,−2)
left parenthesis negative 5 comma 2 right parenthesis and left parenthesis negative 3 comma negative 2 right parenthesis

(−5, 7)
and (−3, 3)
left parenthesis negative 5 comma 7 right parenthesis and left parenthesis negative 3 comma 3 right parenthesis

(−7, 4)
and (−5, 0)
left parenthesis negative 7 comma 4 right parenthesis and left parenthesis negative 5 comma 0 right parenthesis

(1, 2)
and (3,−2)

Answer 1

To translate the line segment with endpoints \((-2, 7)\) and \((0, 3)\) by 3 units to the left and 5 units down, we need to adjust both coordinates of each endpoint.

1. Shift left by 3 units: Subtract 3 from the x-coordinate.
2. Shift down by 5 units: Subtract 5 from the y-coordinate.

Let's perform the translation for each endpoint:

For the endpoint \((-2, 7)\):

• Shift left: \(-2 - 3 = -5\)
• Shift down: \(7 - 5 = 2\)

So, the new coordinates for the first endpoint become \((-5, 2)\).

For the endpoint \((0, 3)\):

• Shift left: \(0 - 3 = -3\)
• Shift down: \(3 - 5 = -2\)

So, the new coordinates for the second endpoint become \((-3, -2)\).

Thus, after the translation, the endpoints of the line segment are: \((-5, 2)\) and \((-3, -2)\).

The correct response is: \((-5, 2)\) and \((-3, -2)\).