Two geometry questions in the attached photos - If I have a line, do I have a plane? & If I have three points, do I always have a plane?

Answer:

18) A: only if you have an additional point not on the line.

19) D: No, because all the points may be on the same line.

Step-by-step explanation:

There are basically 4 ways we can determine a plane and they are;

- When we have three non - collinear points: What this means is that if we have three points that are not on one line, then it means that only one particular plane can pass through those points.

- When we have a line and a point that's not on the line

- When we have two lines that intersect each other.

- When we have two lines that are parallel to each other.

From the four conditions above, we can now answer the question;

18) You can only have a plane if there is an additional point not on the line.

Option A

19) Having just three points may not always be sufficient to have a plane because it's possible that the three points may be on the same line which is not a condition for a plane. Thus, option D is correct.

The following statement tells one way to map preimage points to image points when performing a transformation in the coordinate plane. (x, y) → (x + 8, y − 3) This can be read, “The point with coordinates (x, y) is mapped to the point with coordinates (x, y) → (x + 8, y − 3).” With this transformaƟon, for example, (3, 5) is mapped to (3 + 8, 5 – 3) or (11, 2). The figure below shows how the triangle ABC is mapped to A′B′C′. Notice that the pre‐image and image appear to be congruent. Directions: Answer the following questions, showing all pertinent work. Paul has a 40 ft. by 30 ft. pole barn on his farm that he wants to move. The southeast corner of the pole barn is currently located 50 ft. west and 25 ft. north of the stock tank where the cows get their water. Paul wants to move the pole barn so the southeast corner of the barn is located 80 feet east and 80 feet south of the stock tank. 1. Complete the transformation statement for moving Paul’s pole barn. (x, y)→(x + _______ , y + _______ )

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16 3/8 - 6 7/8

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Choose the algebraic description that maps the image ΔXYZ onto ΔX′Y′Z′. Question options: A)
(x, y) → (x + 6, y – 1)
B)
(x, y) → (x – 5, y – 1)
C)
(x, y) → (x + 5, y – 1)
D)
(x, y) → (x – 6, y – 1)

James cut out four parallelograms, the dimensions of which are shown below. Parallelogram 1 length: 12 in. width: 15 in. diagonal: 20 in. Parallelogram 2 length: 16 in. width: 30 in. diagonal: 34 in. Parallelogram 3 length: 20 in. width: 21 in. diagonal: 29 in. Parallelogram 4 length: 18 in. width: 20 in. diagonal: 26 in. James put the parallelograms together so one vertex from each paper exists on a point, as shown in the circle. 4 parallelograms are put together so that one vertex from each paper exists on a point. Which statement explains whether or not the parallelgrams can be put together so each occupies one-quarter of the area of the circle without overlapping any other pieces? Check all that apply. The quadrilaterals can be placed such that each occupies one-quarter of the circle. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.




THE ANSWER IS B AND E

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O A. one solution
O B. no real number solutions
O C. two solutions
O D. three solutions

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