Question

question 1 (3 points) find the coordinates of triangle abc after a translation of 3 units to the left and 2 units up.

Explanation:

Step1: Identify original coordinates

First, find the original coordinates of points A, B, and C from the grid.

• Point A: Looking at the grid, the x - coordinate (horizontal) is -3 (since it's 3 units to the left of the origin) and the y - coordinate (vertical) is -1 (1 unit below the x - axis). So \( A(-3,-1) \).
• Point B: The x - coordinate is -1 and the y - coordinate is -3. So \( B(-1,-3) \).
• Point C: The x - coordinate is -2 and the y - coordinate is -4. So \( C(-2,-4) \).

Step2: Apply translation rules

A translation of 3 units to the left means we subtract 3 from the x - coordinate, and a translation of 2 units up means we add 2 to the y - coordinate. The translation rule is \( (x,y)\to(x - 3,y + 2) \).

For point A:

Substitute \( x=-3 \) and \( y = - 1 \) into the translation rule.
\( x'=-3-3=-6 \)
\( y'=-1 + 2=1 \)
So the new coordinates of A are \( A'(-6,1) \).

For point B:

Substitute \( x=-1 \) and \( y=-3 \) into the translation rule.
\( x'=-1-3=-4 \)
\( y'=-3 + 2=-1 \)
So the new coordinates of B are \( B'(-4,-1) \).

For point C:

Substitute \( x=-2 \) and \( y = - 4 \) into the translation rule.
\( x'=-2-3=-5 \)
\( y'=-4 + 2=-2 \)
So the new coordinates of C are \( C'(-5,-2) \).

Answer:

After translation, the coordinates of triangle \( ABC \) are \( A'(-6,1) \), \( B'(-4,-1) \), and \( C'(-5,-2) \).