4.10 Unit Test Analytic Geometry

Question: What is the area of the rectangle?

60 units²

66 units²

70 units²

74 units²

Answer: 74 units²

Question: What is the area of a triangle whose vertices are J(−2, 1)J(−2, 1), K(0, 3)K(0, 3), and L(4, −4)L(4, −4)?

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Answer: 15

Question: The coordinates of the vertices of a polygon are (−2,−2)(−2,−2), (3,−3)(3,−3), (4,−6)(4,−6), (1,−6)(1,−6), and (−2,−4)(−2,−4).

What is the perimeter of the polygon to the nearest tenth of a unit?

15.3 units

16.9 units

17.5 units

17.9 units

Answer: 16.9 units

Question: Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line −x+4y=20?

Drag each choice into the boxes to correctly complete the table.

Parallel

Perpendicular

Neither

−x+4y=8

y=−4x−3

4x+y=−1

y=−14x+6

Answer: Parallel: −x+4y=8

Perpendicular: y=−4x−3, 4x+y=−1

Neither: y=−14x+6

Question: Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is 2/5?

Drag each choice into the boxes to correctly complete the table.

Parallel

Perpendicular

Neither

line p, with slope 2/5

line n, with slope −5/2

line m, with slope 5/2

line q, with slope −2/5

Answer: Parallel: line p, with slope 2/5

Perpendicular: line n, with slope −5/2

Neither: line m, with slope 5/2

line q, with slope −2/5

Question: The equation of line m is 4x+5y=−2

What is the slope of a line that is perpendicular to line m?

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Answer: 5/4

Question: What is the equation of a line that is parallel to 2x+3y=3 and passes through the point (3, −4)?

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Answer: y=−2/3x−2

Question: What is the equation of a line that is perpendicular to 2x+y=−4 and passes through the point (2, −8)?

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Answer: y=1/2x−9

Question: In △ABC, the coordinates of vertices A and B are A(−2,4) and B(−1,1).

For each of the given coordinates of vertex C, is △ABC a right triangle?

Select Right Triangle or Not a Right Triangle for each set of coordinates.

Right Triangle

Not a Right Triangle

C(2,2)

C(0,4)

C(−2,1)

Answer: Right: C(2,2), C(−2,1)

Not Right: C(0,4)

Question:

Answer: The slope of AB is -7/4, the slope of BC is 1/7, the slope of CD is -5/3, and the slope of AD is 1/2. Quadrilateral ABCD is neither a parallelogram nor a trapezoid because neither pair of opposite sides is parallel.