Translate triangle ABC 2 units right and 4 units down.
Triangle ABC is on a Cartesian plane grid within quadrants I and II.
What are the coordinates for point A′?
A. (0, –3)
B. (–3, 0)
C. (2, –1)
D. (–1, 2)
To translate a point 2 units right and 4 units down, we add 2 to the x-coordinate and subtract 4 from the y-coordinate.
Therefore, if A has coordinates (x,y), A' will have coordinates (x+2, y-4).
Since we don't know the coordinates of A, we can't calculate A' directly.
Therefore, we need to look at the answer choices and see which one corresponds to the coordinates (x+2, y-4) for some (x,y) that satisfies the given conditions.
Looking at the answer choices:
A. (0, -3): This point is already 4 units down, but it is not 2 units to the right of any point in the triangle.
B. (-3, 0): This point is not 4 units down or 2 units to the right of any point in the triangle.
C. (2, -1): If A has coordinates (0,3), then A' would have coordinates (2,-1). This is a valid translation of the triangle.
D. (-1, 2): This point is not 4 units down or 2 units to the right of any point in the triangle.
Therefore, the answer is C. (2,-1).
Question 15 of 19
What is the area of the triangle?
A triangle is shown with a horizontal base labeled 8.7 feet and a dashed line extending upward from this base to the opposite vertex labeled 4.5 feet.
A. 13.2 ft2
B. 19.575 ft2
C. 20.25 ft2
D. 39.15 ft2
15 / 19
14 of 19 Answered
The area of a triangle is given by the formula:
Area = (1/2) x base x height
In this case, the base is 8.7 feet and the height is 4.5 feet. Therefore, we have:
Area = (1/2) x 8.7 x 4.5
Area = 19.575 square feet
Therefore, the answer is B. 19.575 ft2.
Question 18 of 19
Identify a sequence of transformations that maps triangle ABC onto triangle A′′B′′C′′ in the image below.
A coordinate graph is shown.
• Blue triangle A B C is graphed. Point A is located at the point 1 comma 0. Point B is located at the point negative 1 comma 0. Point C is located at the point 0 comma approximately 1.8.
• Red triangle A B C is graphed. Point A double prime is located at the point 0 comma 3. Point B double prime is located at the point negative 0 comma negative 3. Point C double prime is located at the point approximately negative 5.2 comma approximately 0.
A. clockwise 90° rotation; enlargement
B. counterclockwise 90° rotation; reduction
C. counterclockwise 90° rotation; enlargement
D. clockwise 90° rotation; reduction
Looking at the image, it appears that the blue triangle has been rotated and then enlarged/reduced to create the red triangle.
The rotation appears to be either clockwise or counterclockwise 90°. It's hard to determine whether it's clockwise or counterclockwise based on the image alone.
The enlargement/reduction is also a little tricky to determine based on the image, but we can see that the side lengths of the red triangle are approximately three times the side lengths of the blue triangle.
Therefore, the sequence of transformations that maps triangle ABC onto triangle A''B''C'' is either:
B. counterclockwise 90° rotation; reduction
or
D. clockwise 90° rotation; reduction
Both of these options involve a rotation followed by a reduction, which matches what we see in the image.
Write a sequence of transformations that maps quadrilateral ABCD onto quadrilateral A''B''C''D''in the picture below.
Two quadrilaterals are graphed on a coordinate plane.
Since quadrilateral ABCD and A''B''C''D'' are already on a coordinate plane, we can use the coordinate points to determine the sequence of transformations that maps one onto the other.
One possible sequence of transformations is:
1. Reflect quadrilateral ABCD across the x-axis to create quadrilateral A'B'CD.
2. Rotate quadrilateral A'B'CD 90 degrees counterclockwise about the origin to create quadrilateral A''B''C''D'.
Therefore, the sequence of transformations that maps quadrilateral ABCD onto A''B''C''D'' is a reflection across the x-axis followed by a counterclockwise 90-degree rotation about the origin.
Shorter please as short as you can while getting to the point
Reflect quadrilateral ABCD across the x-axis and then rotate it 90 degrees counterclockwise about the origin to get quadrilateral A''B''C''D''.
To translate a point on a Cartesian plane, you need to shift it horizontally (left or right) and vertically (up or down) by the given amounts.
In this case, we are asked to translate the point A (triangle vertex) 2 units to the right and 4 units down.
To find the coordinates for A', we can start with the coordinates for A and apply the translation.
The original coordinates for point A are not given, so we can't directly calculate the new coordinates. However, we know that triangle ABC is on the Cartesian plane within quadrants I and II.
Since A is being translated to the right (positive x-direction) and down (negative y-direction), we can determine that A is located in quadrant I.
Using the given answer choices:
A. (0, –3): This represents a point in quadrant III (negative x and negative y values), which is not consistent with A being in quadrant I.
B. (–3, 0): This represents a point in quadrant II (negative x and positive y values), which is not consistent with A being in quadrant I.
C. (2, –1): This represents a point in quadrant IV (positive x and negative y values), which is not consistent with A being in quadrant I.
D. (–1, 2): This represents a point in quadrant II (negative x and positive y values), which is not consistent with A being in quadrant I.
Since none of the answer choices match with the condition that point A is located in quadrant I, none of the given answer choices are the correct coordinates for A'.
Therefore, without knowing the original coordinates for point A, we cannot determine the exact coordinates for A' based on the given answer choices.