1. Questions

geometry

1. Which of the following is the correct equation for the Pythagorean Theorem, where a and b are the side lengths and c is the length of the hypotenuse?
A. (a-b)^2=c^2
B. a^2-b^2=c^2
C. a^2+b^2=c^2 *******
D. (a+b)^2=c^2

2. Given the following information, can you find the coordinates of the unknown point? Explain.
Two points are 14 units apart. The first point is located at (0,7).
A. The unknown point is (12, 0). Substituting into the Pythagorean Theorem gives 14^2=a^2+7^2. Solving this for a gives a value of approximately 12.
B. The unknown point is (0, 21). Since the first point is located on the y-axis, the second point would be located 14 units away from it, also on the y-axis.
C. The unknown point cannot be found. Neither the distance formula nor the Pythagorean Theorem can be sued to work backwards from a distance to find the coordinates of a point. ******
D. The unknown point cannot be found. When substituting into the distance formula, there will be two unknowns, the x-coordinate and the y-coordinate of the unknown point.

3. Find the distance between the points (9,−7) and (5,−4).
A. 25
B. √7
C. 5 *******
D. √137

4. To find the distance between (17,3) and (17,−5), Marcia used the following equation. Is Marcia correct? Explain.
D = | 3 - (- 5) | = 8
A. Marcia is not correct. According to the distance formula, the distance should be
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√ (-17-17)^2+(3-(-5))^2=√8 (I hope you understand what I tried to do here) **********

B. Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.
C. Marcia is not correct. Since the points are in two-dimensions, the distance formula must be used to find the distance.
D. Marcia is correct. For any pair of points, the distance between the points can be treated as if they are in one-dimension.

5. Which of the following is the correct formula for distance?
A. d=
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√ x2-x1)+(y2-y1), where d is the distance between points (x1,y1) and (x2,y2). *******
B. d=
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√ x2-x1)^2 +(y2-y1)^2, where d is the distance between points (x1,y1) and (x2,y2).
C. d= (x2−x1)^2+(y2−y1)^2, where d is the distance between points (x1,y1) and (x2,y2).
D. d=
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√ x2+x1)^2+(y2+y1)^2, where d is the distance between points (x1,y1) and (x2,y2).

If someone could check over these, maybe even just a couple of them, maybe even just one of them, it would be so greatly appreciated. I'm having a really tough time. Thank you so so much