Let's go through each question one by one:
1. To find the distance between two points, you can use the distance formula. The formula is √((x2 - x1)² + (y2 - y1)²). Let's calculate:
For the points (-13, -8) and (6, 17):
Distance = √((6 - (-13))² + (17 - (-8))²)
= √(19² + 25²)
= √(361 + 625)
= √986
≈ 31.4
So, the correct answer is c. 31.4. You got it right!
2. Applying the same distance formula to points (-10, -8) and (-3, 12):
Distance = √((-3 - (-10))² + (12 - (-8))²)
= √(7² + 20²)
= √(49 + 400)
= √449
≈ 21.2
Therefore, the correct answer is b. 21.2. You got it right again!
3. To find the coordinates of the midpoint of a segment, you can use the midpoint formula. The formula is ((x1 + x2) / 2, (y1 + y2)/ 2).
For the points G(-7, 7) and H(-1, 7):
Midpoint = ((-7 + (-1)) / 2, (7 + 7) / 2)
= (-8 / 2, 14 / 2)
= (-4, 7)
So, the correct answer is c. (-4, 7). You didn't get it right; the correct answer is not a.
4. Using the midpoint formula for points A(4, 12) and B(2, -2):
Midpoint = ((4 + 2) / 2, (12 + (-2)) / 2)
= (6 / 2, 10 / 2)
= (3, 5)
The correct answer is b. (3, 5). You didn't get it right; the correct answer is not c.
So, in summary:
1. You got it right! The answer is c. 31.4.
2. You got it right! The answer is b. 21.2.
3. You got it wrong. The correct answer is c. (-4, 7).
4. You got it wrong. The correct answer is b. (3, 5).
I hope this helps! If you have any more questions or need further clarification, feel free to ask.