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) .
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 \((-3, -2)\)