Unit 6 Task Assessment

Geometry Standards

HSG-GPE.A: Work with geometric descriptions and the equation for a conic section
HSG-CO.A: Experiment with transformations in the plane

1. The parabola in the image has its focus at (4, 3). Its directrix is the line y = 1. The point (8, 6) is on the parabola.

Select all of the statements that are true.

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A
The equation (x - 4) + (y - 3) = y represents this parabola.
B
The equation (x - 4) + (y - 3) = (y - 1) represents this parabola.
C
The point (8, 6) is the same distance from the point (4, 3) as it is from the line y = 1.
D
The point (2, 3) is on the parabola.
E
The point (0.5, 5) is on the parabola.
F
If point (x, y) is on the parabola, then the distance between (x, y) and the point (4, 3) is the same as the distance between (x, y) and the y-axis.

2. Line m is represented by the equation: y + 2 = (x + 4) Select all equations that represent lines perpendicular to line m.

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3. The image shows a circle with center (4, 6) and radius 10 units.

4. Find the center and radius of the circle given by this equation: x - 10x + y + 6y - 30 = 0

5. Figure F is graphed.

a. Transform figure F using the rule (x, y) (-x, y - 8).

b. Describe the transformation precisely.

c. Does the transformation result in a figure that is congruent to the original, similar to the original, or neither?