A translation is shown on the grid below.
On a coordinate plane, triangle A B C has points (negative 4, 2), (negative 4, negative 2), (negative 1, negative 2). Triangle A prime B prime C prime has points (1, 5), (1, 1), (4, 1).
Which are true statements about the translation?
Oh, translation! It's like moving a triangle without ruining its shape - the ultimate teleportation trick! Now, let's see which statements are true about this magical translation:
1. The translation shifted the triangle to the right: Well, technically, it did shift to the right, but only after taking a little detour to the left. So, let's say it shuffled to the right in a zigzag fashion!
2. The translation shifted the triangle upwards: Yup, spot on! The triangle decided to take the elevator up and moved in an upward direction, just like those Monday morning moods.
3. The translation maintained the same shape: Absolutely, no funny business here! The triangle kept its fancy little angles and sides intact. It didn't morph into a square or start doing somersaults. Good on it!
So, we have two true statements about the translation: it shifted to the right (with a detour) and upwards, while keeping its snazzy shape. Triangle teleportation complete!
To determine the true statements about the translation from triangle ABC to triangle A' B' C', we need to compare the corresponding vertices.
Let's analyze the coordinates of each pair of corresponding points:
- The point A (-4, 2) is translated to A' (1, 5).
- The point B (-4, -2) is translated to B' (1, 1).
- The point C (-1, -2) is translated to C' (4, 1).
Based on this information, we can make the following observations:
1. The x-coordinates of A and A' differ by 5 units.
2. The y-coordinates of A and A' differ by 3 units.
3. The x-coordinates of B and B' differ by 5 units.
4. The y-coordinates of B and B' differ by 3 units.
5. The x-coordinates of C and C' differ by 5 units.
6. The y-coordinates of C and C' differ by 3 units.
From these observations, we can conclude that the translation is a shift 5 units to the right and 3 units upwards.
To determine the true statements about the translation between triangle ABC and triangle A'B'C', we need to compare the coordinates of the corresponding points.
Let's analyze each statement:
1. The translation is a reflection:
To determine if the translation is a reflection, we need to compare the x-coordinates of the corresponding points. In this case, the x-coordinates of triangle ABC are all negative, while the x-coordinates of triangle A'B'C' are all positive. Therefore, this statement is false.
2. The translation is a rotation:
To determine if the translation is a rotation, we need to analyze the relationship between the corresponding angles and sides of the triangles. Since the given problem does not provide any information about angles or side lengths, we cannot determine if the translation is a rotation. Therefore, this statement is inconclusive.
3. The translation is a dilation:
To determine if the translation is a dilation, we need to compare the corresponding side lengths. Unfortunately, the problem does not provide any side lengths to compare. Therefore, we cannot determine if the translation is a dilation. This statement is inconclusive.
4. The translation is a translation:
Given that the problem specifically mentions a translation and the coordinates of the points are indeed translated, we can conclude that this statement is true. The coordinates of triangle ABC have been translated to obtain triangle A'B'C'.
To summarize, the true statement about the translation is that it is a translation. The other statements (reflection, rotation, and dilation) cannot be concluded based on the given information.
Ever think of using numbers instead of words for a simple math problem? You have
C = (-1,-2)
C' = (4,1)
(-4,-2) + (h,k) = (4,1)
so,
-4+h = 4
-2+k = 1
so the translation T = (x,y) → (x+8,y+3)
now go for your questions/statements.