Find the value of x and y
1 answer:
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Answer:
Step-by-step explanation:
we know that
The graph of the figure represent a vertical parabola open upward
The vertex represent a minimum
The vertex of the quadratic equation is the point (h,k)
The range of the quadratic equation is the interval for y [k,∞)
Looking at the graph
The vertex is the point (0,-6)
therefore
The range is the interval [-6,∞)
Answer:
7) K'(1, 1), N'(4, 0), Q'(4, 4)
9) F'(4, 2), W'(4, 5), K'(3, 2)
Step-by-step explanation:
When you are not sure about reflections and rotations, it can be useful to actually draw a graph. The line of reflection is the perpendicular bisector of the segment connecting a point with its image. That is, the image is the same distance from the line on the other side. A point that is <em>on</em> the line of reflection is "invariant," it doesn't move.
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7) Reflecting across the x-axis changes the sign of the y-coordinate. That is all. Any point on the x-axis (y=0) is unchanged. The transformation is ...
(x, y) ⇒ (x, -y)
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9) Reflecting across a vertical line changes the x-coordinate. The new value of x will be ...
x' = 6 - x
The "6" is double the x-coordinate of the vertical line. The transformation is ...
(x, y) ⇒ (6-x, y)
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<em>Derivation of the formula for reflection on x=3</em>
In general if M is the midpoint of a point (A) and its reflection (A'), then we have ...
M = (A +A')/2
2M = A + A'
2M -A = A'
When a point is reflected across a vertical line, all of the y-coordinate values remain unchanged. So, for A=(x, y) and M=(3, y), we have ...
A' = 2(3, y) -(x, y) = (6-x, 2y-y)
A' = (6 -x, y)
So, the reflection transformation across the line x = 3 is ...
(x, y) ⇒ (6-x, y)
Answer:
Option (C)
Step-by-step explanation:
If AD is the altitude to BC, both the segments AD and BC will be perpendicular to each other.
By the property of perpendicular lines,
where is the slope of the line AD and
is the slope of BC.
Now from the given property,
Therefore, slope of altitude BC =
Option (C) will be the answer.