Triangle ABC is shown on the coordinate grid.
Explanation: The figure shows a triangle Upper Word ABC on the coordinate grid. The values on the x-axis range from negative 8 to 8 in increments of 2 and the values on the y-axis range from negative 8 to 8 in increments of 2. The coordinates of the vertices Upper A, Upper B, and Upper C are labeled as (negative 4, 1), (negative 1, 1), and (negative 1, 4) respectively.
Part A
Translate ΔABC 6 units horizontally. How are the values in the ordered pairs affected by the translation?
Part B
Translate ΔABC −3 units vertically. How are the values in the ordered pairs affected by the translation?
Part C
How could you determine the coordinates of the vertices of a translated image without using a graph?
Please help, i'm confused.
Geesh, why not just type:
Given: Triangle ABC with vertices A(-4,1), B(-1,1) and C(-1,4)
Part A
Translate ΔABC 6 units horizontally:
the x value of each point would increase by 6, the y's would stay the same
e.g. A(-1,4) -----> A'(5,4)
etc
Part B
You do it in the same way
Part C, I just did it without a graph.
Part A: When translating ΔABC 6 units horizontally, the x-coordinate of each vertex will increase by 6 units. So, the new coordinates of the vertices will be:
A: (-4 + 6, 1) = (2, 1)
B: (-1 + 6, 1) = (5, 1)
C: (-1 + 6, 4) = (5, 4)
Part B: When translating ΔABC -3 units vertically, the y-coordinate of each vertex will decrease by 3 units. So, the new coordinates of the vertices will be:
A: (2, 1 - 3) = (2, -2)
B: (5, 1 - 3) = (5, -2)
C: (5, 4 - 3) = (5, 1)
Part C: To determine the coordinates of the vertices of a translated image without using a graph, you can add or subtract the desired amounts to the x and y coordinates of each vertex. For example, if you want to translate a triangle 3 units to the left and 2 units down, you would subtract 3 from the x-coordinate and subtract 2 from the y-coordinate of each vertex. This allows you to determine the new coordinates of the translated triangle without needing a graph.
Part A:
To translate Triangle ABC 6 units horizontally, we need to add 6 to the x-coordinate of each vertex while keeping the y-coordinate the same.
The original coordinates of the vertices are:
A (-4, 1)
B (-1, 1)
C (-1, 4)
Adding 6 to the x-coordinate of each vertex, we get the new coordinates:
A' (-4 + 6, 1) = (2, 1)
B' (-1 + 6, 1) = (5, 1)
C' (-1 + 6, 4) = (5, 4)
So the new coordinates of Triangle A'B'C' after the horizontal translation are:
A' (2, 1)
B' (5, 1)
C' (5, 4)
Part B:
To translate Triangle ABC -3 units vertically, we need to subtract 3 from the y-coordinate of each vertex while keeping the x-coordinate the same.
The original coordinates of the vertices of Triangle ABC are:
A (-4, 1)
B (-1, 1)
C (-1, 4)
Subtracting 3 from the y-coordinate of each vertex, we get the new coordinates:
A'' (-4, 1 - 3) = (-4, -2)
B'' (-1, 1 - 3) = (-1, -2)
C'' (-1, 4 - 3) = (-1, 1)
So the new coordinates of Triangle A''B''C'' after the vertical translation are:
A'' (-4, -2)
B'' (-1, -2)
C'' (-1, 1)
Part C:
To determine the coordinates of the vertices of a translated image without using a graph, we can use the concept of vector addition.
For example, let's say we want to translate Triangle ABC by a vector (3, -2). The vector represents the translation in the x-direction and y-direction. To determine the new coordinates of the vertices, we add the corresponding components of the vector to the original coordinates.
The original coordinates of the vertices of Triangle ABC are:
A (-4, 1)
B (-1, 1)
C (-1, 4)
Adding (3, -2) to the x-coordinate and y-coordinate of each vertex, we get the new coordinates:
A''' (-4 + 3, 1 - 2) = (-1, -1)
B''' (-1 + 3, 1 - 2) = (2, -1)
C''' (-1 + 3, 4 - 2) = (2, 2)
So the new coordinates of Triangle A'''B'''C''' after the translation are:
A''' (-1, -1)
B''' (2, -1)
C''' (2, 2)
By using vector addition, we can determine the coordinates of the vertices of a translated image without relying on a graph.