What is the area of a circle whose radius is x + 2?
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Given:
AD is diameter of the circle, AB is the tangent, and measure of arc ADC is 228 degrees.
To find:
The and
.
Solution:
AD is diameter of the circle. So, the measure of arc AD is 180 degrees.
The measure inscribed angle is half of the corresponding subtended arc.
AB is the tangent. So, because radius is perpendicular on the tangent and the point of tangency.
Therefore, and
.
The x-coordinates of will be the negation of the x-coordinates of
The line segment from S to the y-axis equals the line segment from S' to the y-axis. Similarly, the line segment from T to the y-axis equals the line segment from T' to the y-axis
See attachment for and
In order to solve this question, I will make the following assumptions.
Assume that the coordinates of are
Refer to attachment for illustrations
<u>(1) Reflect </u><u> over y-axis and describe the transformation</u>
To reflect across the y-axis, the following rule must be followed
This means that:
<u>The description of the </u><u>transformation </u><u>is as follows:</u>
Notice that the signs of the x-coordinates and
of both triangles are different.
In other words, if the x-coordinate of one is positive, then the other will have a negative x-coordinate; and vice versa.
<u>(2) Compare the segments and the line of reflection</u>
To reflect across the y-axis means that the reflecting line is the y-axis, itself.
The distance between a point to the y-axis is the absolute value of the x-coordinate.
So, the distance between S and the y-axis is:
The distance between S' and the y-axis is:
We can conclude that the two line segments are equal.
This is the same for other point T and T' because of the formula used above.
<u>From T and T' to the y-axis is:</u>
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