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) .

Question

1. (−5, 2) and (−3,−2)
2. (−5, 7) and (−3, 3)
3. (1, 2) and (3,−2)
4. (−7, 4) and (−5, 0)

Answer 1

To demonstrate the translation of a line segment, we need to move each endpoint by the specified amounts: 3 units to the left and 5 units down.

Translation Operation:

• Moving to the left by 3 units means we subtract 3 from the x-coordinates.
• Moving down by 5 units means we subtract 5 from the y-coordinates.

Given endpoints:

• Endpoint 1: \((-2, 7)\)
• Endpoint 2: \((0, 3)\)

Applying the translation:

1. Translating point \((-2, 7)\): \[ x: -2 - 3 = -5 \ y: 7 - 5 = 2 \] So, the new position of the first endpoint is \((-5, 2)\).

2. Translating point \((0, 3)\): \[ x: 0 - 3 = -3 \ y: 3 - 5 = -2 \] So, the new position of the second endpoint is \((-3, -2)\).

Translated Endpoints: The translated endpoints are \((-5, 2)\) and \((-3, -2)\).

Answer:

1. \((-5, 2)\) and \((-3, -2)\)