Rotations Quiz
1. Name the segment which is congruent to line BC.
C - line MN
2. What image is the translation of the shown triangle given by the translation rule (x,y) = (x-2, y+3)
C - (its higher(more y) and more to the left(less x))
3. The vertices of a rectangle are R(-5,-5), S(-1,-5), T(-5,1). After translation, R' is the point (-11,-11). Find the translation rule and coordinates of U'.
4. Which describes the translation represented by the translation rule (x,y) = (x-7, y-7)
A - 7 unites to the left and7 units down
5. Sarah was sitting in a seat at a baseball game when another ticket holder showed her she was in the wrong seat. The other ticket holder kindly told Sarah she needed to go 5 rows down and3 seats to the right. Which rule describes the translation needed to put sarah in the correct seat?
D (x,y) = (x +3 ,y-5)
6. What translation rule can be used to describe the result of the composition of (x,y) = (x-9, y-2) and (x,y) = ( x+1 y-2 )
C - (x,y) = (x-8, y-4)
7. The vertices of a triangle are P(_7, _4), Q(-7,-8), and R(3,-3). Name the vertices of the image reflected across the line y=x
C - P' (-4,-7), Q (-8,-7), R (-3 , 3)
8. Find the image of O(-2,-1) after two translations, First across the line y= -5 , and then across the line x=1.
C - 4, -9
The hexagon gikmpr and triangle fjn are regular. the dashed line segments form 30 angles
9. D - OF
(from here and below i wont write the questions)
10. D - 72 degrees
11. C - Rotation
there were only 2 but whatever, i also wont give any notes so yeah...
But question 3 b
12. B - 90 degrees
Lifesaver bro
Thanks question 9 is OG and 10 is 180
To find the answers to the questions on the Rotations Quiz, here are the explanations for each question:
1. To find the segment congruent to line BC, you need to look for a segment with the same length as line BC. Compare the lengths of line BC with the lengths of the other line segments provided until you find a match. In this case, line MN is congruent to line BC.
2. To determine the image of the triangle after the translation given by the translation rule (x,y) = (x-2, y+3), you need to apply the translation rule to each vertex of the triangle. Subtract 2 from the x-coordinate and add 3 to the y-coordinate of each vertex. The resulting coordinates of the triangle vertices will be the image after the translation.
3. Given the coordinates of the rectangle's vertices before and after the translation, you can find the translation rule and the coordinates of U' by finding the difference between the coordinates of R and R'. Subtract the x-coordinate of R' from the x-coordinate of R to find the horizontal translation, and subtract the y-coordinate of R' from the y-coordinate of R to find the vertical translation. Apply these differences to the coordinates of U to find U'.
4. The translation rule (x,y) = (x-7, y-7) means that every point should be shifted 7 units to the left (subtract 7 from the x-coordinate) and 7 units down (subtract 7 from the y-coordinate) to determine the image after the translation.
5. The rule (x,y) = (x +3 ,y-5) describes the translation needed to put Sarah in the correct seat. The rule means that Sarah needs to move 3 seats to the right (add 3 to the x-coordinate) and 5 rows down (subtract 5 from the y-coordinate) to reach the correct seat.
6. To determine the translation rule for the composition of two translations, you need to apply the first translation rule followed by the second translation rule. For example, for the composition of (x,y) = (x-9, y-2) and (x,y) = ( x+1, y-2), apply the first translation rule and then the second translation rule to get the final translation rule: (x,y) = (x-8, y-4).
7. To find the image of the triangle reflected across the line y=x, you need to swap the x and y coordinates for each vertex. The new coordinates will give you the reflected image of the triangle.
8. To find the image of point O after two translations, first across the line y=-5 and then across the line x=1, apply each translation rule to the original coordinates of O. Start with the translation across the line y=-5, which means shifting the point 5 units downward (subtract 5 from the original y-coordinate). Then, apply the translation across the line x=1, which means shifting the point 1 unit to the right (add 1 to the modified x-coordinate). The resulting coordinates will give you the image of O after the two translations.
9. Triangle FJN is regular, meaning all angles are congruent. To find the dashed line segment that forms a 30-degree angle with the side of the hexagon, locate the corner of the hexagon where the dashed line segment starts, then count 30 degrees in a clockwise direction to find the corresponding dashed line segment. In this case, segment OF forms a 30-degree angle with the side of the hexagon.
10. To find the measure of the angle formed by the dashed line segment and the side of the hexagon, count the number of degrees between the dashed line segment and the side of the hexagon. In this case, the measure of the angle is 72 degrees.
11. Based on the given information, the transformation that was most likely used to create the triangle FJN from the hexagon GIKMPR is a rotation. A rotation involves rotating an object around a fixed point by a certain angle. In this case, the object rotated 30 degrees around point O to form the triangle FJN.
Remember, to solve these types of questions effectively, it's important to understand the concepts of translations, reflections, rotations, and congruence, as well as practice applying the rules and principles involved.