A has the coordinates (–4, 3) and B has the coordinates (4, 4). If DO,1/2(x, y) is a dilation of △ABC, what is true about the im
age △A'B'C'? Check all that apply.
AB is parallel to A'B'.
DO,1/2(x, y) = (1/2x, 1/2y)
The distance from A' to the origin is half the distance from A to the origin.
The vertices of the image are farther from the origin than those of the pre-image.
A'B' is greater than AB.
AB is parallel to A'B'.
DO,1/2(x, y) = (1/2x, 1/2y)
The distance from A' to the origin is half the distance from A to the origin.
The vertices of the image are farther from the origin than those of the pre-image.
A'B' is greater than AB.
2 answers:
A dilation represents a transformation 
, centered at point O with a scale factor of k, which cannot be zero. This transformation keeps O fixed while transforming any other point P into its image P'. Points O, P, and P' are collinear.
In a dilation of
, the scale factor 
maps the original figure to its transformed image in such a way that the distances from O to points of the image are half the distances from O to the original figure. Consequently, the image's size is also half that of the original figure.
Thus, <span>If represents the dilation of △ABC, then the properties of the image △A'B'C'</span> are:
<span>AB is parallel to A'B'.
The distance from A' to the origin is half that from A to the origin.</span>
In a dilation of
Thus, <span>If
<span>AB is parallel to A'B'.
The distance from A' to the origin is half that from A to the origin.</span>
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The sine function that corresponds to the scenario is y = 6sin((π / 10) x) - 10.
Step-by-step explanation:
The general equation for a sine function is Asin(Bx)+C.
A buoy rises and drops 6 meters, indicating a vertical and horizontal movement of 6 meters—this is the amplitude.
Thus, the amplitude A is 6.
The period is defined as the horizontal distance for one complete wave cycle.
The buoy takes 10 seconds to go from its peak to its lowest point (half a cycle).
Hence, the total period for a complete cycle is 20 seconds.
Additionally, Period = 2π divided by B.
Thus, 20 (B) = 2π.
This results in B being equal to 2π / 20.
= π / 10.
Since the buoy operates at a depth of 10 meters, C equals -10.
<pinserting all="" values="" into="" the="" formula="" yields:="">⇒y = 6sin((π/10)x) - 10.
The first point marks the midline,
When x=0,
⇒y=6sin(0)-10.
y= -10.
∴ Thus, the line begins at y = -10.
The consecutive point will represent the maximum or minimum value.
Those are (5,-4) and (15, -16.)
