Square ABCD is dilated by a scale factor of 2 with the center of dilation at the origin to form square ABCD . What are the coord
inates of vertex B. A(2,7) C(8,1) D(2,1)
1 answer:
Answer:
B'(16,14)
Step-by-step explanation:
In square ABCD, A(2,7) C(8,1) D(2,1). First, find the coordinates of the vertex B. From the attached diagram you can see that CD=6 units and is parallel to the x-axis, AD=6 units and is parallel to the y-axis. So, B(8,7).
The origin O is the center of dilation, 2 is the scale factor. The rule of the dilation is
(x,y)→(2x,2y)
Thus,
B(8,7)→B'(16,14) (see attached figure).
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Answer:
1. 6 feet
2. 6.25 feet
3. 1 feet
4. 6 feet
Step-by-step explanation:
The equation is :
1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.
So, substituting x = 0 in the equation, we get
So, the diving board is 6 feet above the surface of the water.
2. From the equation, we known that it is a parabola and the vertex is minimum.
It is the minimum height which represents the depth Kendra dives into the water.
So the coordinate of the vertex is =
Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,
a = 1 and b = -7
∴ x coordinate =
Now substituting to find f(x),
= -6.25
Therefore, the diver dives 6.25 feet below the water surface.
3. The horizontal distance from the board the diver enters into the water.
This is the y-intercept and it is the value of x when h(x)=0.
∴
Factorizing, we get
∴
So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.
4. We know that the equation given has x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height
. The height is the water surface level.
The first x intercept represents the points where Kendra dives into the water.
And the second x intercept is the point where Kendra comes out of the water surface. This this is for
.
Thus Kendra dives out of the water surface at 6 feet from the board.