SAT Math : Coordinate Geometry
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Example Questions
Example Question #4 : Transformation
The following is an equation of a circle:
If this circle is moved to the left 2 spaces and down 3 spaces, where does the center of the new circle lie?
The general formula for a circle with center (h,k) and radius r is 
The center of the original circle, therefore, is (2, -4).
If we move the circle to the left 2 spaces and down 3 spaces, then the center of the new circle is given by 
Example Question #1 : Transformation
Let f(x) = x3 – 2x2 + x +4. If g(x) is obtained by reflecting f(x) across the y-axis, then which of the following is equal to g(x)?
x3 – 2x2 – x + 4
–x3 – 2x2 – x + 4
x3 + 2x2 + x + 4
–x3 – 2x2 – x – 4
–x3 + 2x2 – x + 4
–x3 – 2x2 – x + 4
In order to reflect a function across the y-axis, all of the x-coordinates of every point on that function must be multiplied by negative one. However, the y-values of each point on the function will not change. Thus, we can represent the reflection of f(x) across the y-axis as f(-x). The figure below shows a generic function (not f(x) given in the problem) that has been reflected across the y-axis, in order to offer a better visual understanding.
Therefore, g(x) = f(–x).
f(x) = x3 – 2x2 + x – 4
g(x) = f(–x) = (–x)3 – 2(–x)2 + (–x) + 4
g(x) = (–1)3x3 –2(–1)2x2 – x + 4
g(x) = –x3 –2x2 –x + 4.
The answer is –x3 –2x2 –x + 4.
Example Question #8 : How To Find Transformation For An Analytic Geometry Equation
Bobby draws a circle on graph paper with a center at (2, 5) and a radius of 10.
Jenny moves Bobby's circle up 2 units and to the right 1 unit.
What is the equation of Jenny's circle?
If Jenny moves Bobby's circle up 2 units and to the right 1 unit, then the center of her circle is (3, 7). The radius remains 10.
The general equation for a circle with center (h, k) and radius r is given by
For Jenny's circle, (h, k) = (3, 7) and r=10.
Substituting these values into the general equation gives us
Example Question #1 : How To Find A Ray
Refer to the above diagram. The plane containing the above figure can be called Plane 
True
False
False
A plane can be named after any three points on the plane that are not on the same line. As seen below, points 
Therefore, Plane 
Example Question #1541 : Basic Geometry
Refer to the above figure.
True or false: 
False
True
True
Two rays are opposite rays, by definition, if
(1) they have the same endpoint, and
(2) their union is a line.
The first letter in the name of a ray refers to its endpoint; the second refers to the name of any other point on the ray. 
The union of the two rays is a line. Both criteria are met, so the rays are indeed opposite.
Example Question #1541 : Basic Geometry
Refer to the above diagram:
True or false: 
False
True
False
A line can be named after any two points it passes through. The line 
The line does not pass through 
Example Question #301 : Coordinate Geometry
Refer to the above diagram.
True or false: 
True
False
False
By definition, two angles comprise a pair of vertical angles if
(1) they have the same vertex; and
(2) the union of the two angles is exactly a pair of intersecting lines.
In the figure below, 
While the two angles have the same vertex, their union is not a pair of intersecting lines. The two angles are not a vertical pair.
Example Question #302 : Coordinate Geometry
Refer to the above diagram.
True or false: 
False
True
False
By definition, two angles form a linear pair if and only if
(1) they have the same vertex;
(2) they share a side; and,
(3) their interiors have no points in common.
In the figure below, 
The two angles have the same vertex and share no interior points. However, they do not share a side. Therefore, they do not comprise a linear pair.
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