8th Grade Math › Geometry
Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?
No
Yes, translation down and to the left
Yes, rotation
Yes, refection over the x-axis
In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.
Also, let's recall the types of transformations:
Rotation: A rotation means turning an image, shape, line, etc. around a central point.
Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.
For this question, we can tell that the triangles are not the same size, the red triangle is smaller; thus, the triangles are not congruent.
Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?
No
Yes, translation down
Yes, rotation
Yes, refection over the x-axis
In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.
Also, let's recall the types of transformations:
Rotation: A rotation means turning an image, shape, line, etc. around a central point.
Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.
For this question, we can tell that the triangles are not the same size, the red triangle is narrower; thus, the triangles are not congruent.
Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.
The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or angle. When a triangle includes a right angle, the triangle is said to be a "right triangle."
We can use the Pythagorean Theorem to help us solve this problem.
The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:
We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:
Calculate the volume of the cone provided. Round the answer to the nearest hundredth.
In order to solve this problem, we need to recall the formula used to calculate the volume of a cone:
Now that we have this formula, we can substitute in the given values and solve:
Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?
Yes, translation to the left
Yes, reflection over the x-axis
Yes, rotation
No
In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.
Also, let's recall the types of transformations:
Rotation: A rotation means turning an image, shape, line, etc. around a central point.
Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.
For this question, we can tell that the triangles are the same size; thus, the triangles are congruent. The red triangle has been moved to the left; thus, the triangle has been translated to the left.
The triangle has not undergone a reflection over the x-axis, because the triangle didn't flip over the x-axis. Also, the triangle has not been rotated because that rotation would have caused the triangle to have its top point facing left or right, not up and down.
Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?
No
Yes, translation down and to the left
Yes, rotation
Yes, refection over the x-axis
In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.
Also, let's recall the types of transformations:
Rotation: A rotation means turning an image, shape, line, etc. around a central point.
Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.
For this question, we can tell that the triangles are not the same size, the red triangle is smaller; thus, the triangles are not congruent.
In order to get to work, Jeff leaves home and drives 4 miles due north, then 3 miles due east, followed by 6 miles due north and, finally, 7 miles due east. What is the straight line distance from Jeff’s work to his home?
2√5
11
10√2
15
6√2
Jeff drives a total of 10 miles north and 10 miles east. Using the Pythagorean theorem (a2+b2=c2), the direct route from Jeff’s home to his work can be calculated. 102+102=c2. 200=c2. √200=c. √100√2=c. 10√2=c
Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?
No
Yes, translation down
Yes, rotation
Yes, refection over the x-axis
In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.
Also, let's recall the types of transformations:
Rotation: A rotation means turning an image, shape, line, etc. around a central point.
Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.
For this question, we can tell that the triangles are not the same size, the red triangle is narrower; thus, the triangles are not congruent.
Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?
No
Yes, translation to the left
Yes, rotation
Yes, refection over the y-axis
In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.
Also, let's recall the types of transformations:
Rotation: A rotation means turning an image, shape, line, etc. around a central point.
Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.
For this question, we can tell that the triangles are not the same size, the red triangle is smaller; thus, the triangles are not congruent.
Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?
Yes, translation to the left
Yes, reflection over the x-axis
Yes, rotation
No
In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.
Also, let's recall the types of transformations:
Rotation: A rotation means turning an image, shape, line, etc. around a central point.
Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.
For this question, we can tell that the triangles are the same size; thus, the triangles are congruent. The red triangle has been moved to the left; thus, the triangle has been translated to the left.
The triangle has not undergone a reflection over the x-axis, because the triangle didn't flip over the x-axis. Also, the triangle has not been rotated because that rotation would have caused the triangle to have its top point facing left or right, not up and down.