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
1. yes
2. All you know is that the point is anywhere on a circle of radius 14 and center at (0,7). I would pick D
3. Yes, 3, 4, 5 right triangle
4. It is 8 units STRAIGHT DOWN (same x). She did it right
5. NO ...... sqrt [ (x2-x1)^2 + (y2-y1)^2 ]
Thank you so much Damon! The quick answers that the Jishka teachers constantly provide help so many students more then you would think and it is so greatly appreciated.
bro yall suck every thing
1. The correct equation for the Pythagorean Theorem is C. a^2 + b^2 = c^2. This theorem states that in a right-angled triangle, the sum of the squares of the lengths of the two shorter sides (a and b) is equal to the square of the length of the hypotenuse (c).
2. The correct answer is C. The unknown point cannot be found. Neither the distance formula nor the Pythagorean Theorem can be used to work backwards from a distance to find the coordinates of a point. The distance between two points only provides information about the length, not the specific coordinates of those points.
3. To find the distance between two points, you can use the distance formula, which is derived from the Pythagorean Theorem. The correct answer is C. The distance between the points (9,-7) and (5,-4) is 5.
Distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, (x1, y1) = (9, -7) and (x2, y2) = (5, -4).
d = √((5 - 9)^2 + (-4 - (-7))^2)
= √((-4)^2 + (3)^2)
= √(16 + 9)
= √25
= 5
4. Marcia is not correct. According to the distance formula, the distance between the points (17, 3) and (17, -5) should be √8. The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, (x1, y1) = (17, 3) and (x2, y2) = (17, -5).
d = √((17 - 17)^2 + (-5 - 3)^2)
= √(0^2 + (-8)^2)
= √(0 + 64)
= √64
= 8
So, the correct distance should be 8, not √8.
5. The correct formula for distance is A. d = √((x2 - x1)^2 + (y2 - y1)^2), where d is the distance between points (x1, y1) and (x2, y2). This formula is the distance formula derived from the Pythagorean Theorem, using the coordinates of two points in a Cartesian plane.