What is the sequence of steps used to move the triangle in quadrant four to the triangle in quadrant two to show that the triangles are congruent. Original position. E (-2, 5) H (-5, 3) G (-2, 3) new position E (1, -1) H (4, -3) G (1, -3)
The options are
A rotation, 90° clockwise in a translation of (1, 6)
B reflection to quadrant three then a translation of (3, 2)
C reflection to quadrant one, then a translation of (3, 2)
D translation to quadrant two then a rotation 90° counterclockwise
Here are the actual answers i promise these are correct .
1 . rotation, then translation
2. Reflection across the y-axis and then a translation of (-3, -5), etc ...
3 . rotation, then translation
4 . rotation, then translation
5 . reflection to Quadrant III etc ...
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The correct answer is D) translation to quadrant two then a rotation 90° counterclockwise.
To show that the triangles are congruent, we need to move the triangle in quadrant four to the triangle in quadrant two using a combination of translation and rotation.
First, we can translate the triangle in quadrant four by adding (3, -2) to each coordinate:
E (-2, 5) → E (1, 3)
H (-5, 3) → H (-2, 1)
G (-2, 3) → G (1, 1)
Now, we can rotate the translated triangle by 90° counterclockwise. This can be done by switching the x and y coordinates and negating the new x coordinate:
E (1, 3) → E (3, 1)
H (-2, 1) → H (-1, -2)
G (1, 1) → G (-1, 3)
The new position of the triangle after translation and rotation is:
E (3, 1)
H (-1, -2)
G (-1, 3)
Comparing this new position with the triangle in quadrant two, we can see that they are congruent.
"<3" is correct guys
To move the triangle in quadrant four to the triangle in quadrant two and show that they are congruent, you can use the following steps:
1. Translation: Move the triangle horizontally and vertically to the new position. In this case, the new position is E(1, -1), H(4, -3), G(1, -3). The translation from the original position to the new position is (x + 3, y - 2). This translates each point of the triangle to the new position.
So far, the options that involve translation are:
B) Reflection to quadrant three then a translation of (3, 2)
C) Reflection to quadrant one, then a translation of (3, 2)
2. Rotation: Rotate the triangle 90° counterclockwise. However, none of the given options involve a rotation, so we can eliminate option D.
Now, let's analyze the remaining options:
A) Rotation, 90° clockwise in a translation of (1, 6) - This option involves a rotation, but the rotation direction is opposite of what is required (counter clockwise instead of clockwise).
B) Reflection to quadrant three then a translation of (3, 2) - This option includes a reflection and a translation. Since the triangle is already in quadrant four, reflecting it to quadrant three means that the x-coordinate will become negative. After the reflection, a translation of (3, 2) is applied. This option does not rotate the triangle, so we can eliminate it.
C) Reflection to quadrant one, then a translation of (3, 2) - This option includes a reflection and a translation. The reflection to quadrant one means that both the x and y coordinates become positive. After the reflection, a translation of (3, 2) is applied. This option does not rotate the triangle.
The correct answer is C) Reflection to quadrant one, then a translation of (3, 2).
b
c
b
a
c
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