Question
What is the length of ModifyingAbove upper A upper B with bar, with endpoints Aleft parenthesis 3 comma 2 right parenthesis and Bleft parenthesis 8 comma 14 right parenthesis?
(1 point)
Responses
StartRoot 37 EndRoot
7
13
StartRoot 509 EndRoot
(1 point)
Responses
StartRoot 37 EndRoot
7
13
StartRoot 509 EndRoot
Answers
GPT 3.5
To find the length of a line segment with endpoints (x1, y1) and (x2, y2), we use the distance formula:
d = √((x2-x1)^2 + (y2-y1)^2)
In this case, A(3, 2) and B(8, 14), so:
d = √((8-3)^2 + (14-2)^2)
d = √(5^2 + 12^2)
d = √(25 + 144)
d = √169
d = 13
So, the length of ModifyingAbove upper A upper B with bar, with endpoints A(3, 2) and B(8, 14) is 13.
d = √((x2-x1)^2 + (y2-y1)^2)
In this case, A(3, 2) and B(8, 14), so:
d = √((8-3)^2 + (14-2)^2)
d = √(5^2 + 12^2)
d = √(25 + 144)
d = √169
d = 13
So, the length of ModifyingAbove upper A upper B with bar, with endpoints A(3, 2) and B(8, 14) is 13.
no name
What is the midpoint of ModifyingAbove upper A upper B with bar, with endpoints Aleft parenthesis 3 comma 2 right parenthesis and Bleft parenthesis 8 comma 14 right parenthesis?
(1 point)
Responses
left parenthesis 5.5 comma 8 right parenthesis
: left parenthesis 2.5 comma 11 right parenthesis
left parenthesis 0.5 comma 3 right parenthesis
left parenthesis 2.5 comma 6 right parenthesis
(1 point)
Responses
left parenthesis 5.5 comma 8 right parenthesis
: left parenthesis 2.5 comma 11 right parenthesis
left parenthesis 0.5 comma 3 right parenthesis
left parenthesis 2.5 comma 6 right parenthesis
GPT 3.5
To find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2), we use the midpoint formula:
midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, A(3, 2) and B(8, 14), so:
midpoint = ((3 + 8)/2, (2 + 14)/2)
midpoint = (11/2, 16/2)
midpoint = (5.5, 8)
So, the midpoint of ModifyingAbove upper A upper B with bar, with endpoints A(3, 2) and B(8, 14) is (5.5, 8).
midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, A(3, 2) and B(8, 14), so:
midpoint = ((3 + 8)/2, (2 + 14)/2)
midpoint = (11/2, 16/2)
midpoint = (5.5, 8)
So, the midpoint of ModifyingAbove upper A upper B with bar, with endpoints A(3, 2) and B(8, 14) is (5.5, 8).
no name
triangle ABC has vertices Aleft parenthesis 1 comma 5 right parenthesis, B left parenthesis 9 comma 7 right parenthesis, and Cleft parenthesis 7 comma 13 right parenthesis. M is the midpoint of ModifyingAbove upper A upper B with bar and N is the midpoint of ModifyingAbove upper B upper C with bar. Which of the following is the length of ModifyingAbove upper M upper N with bar?
(1 point)
Responses
3
4
5
6
(1 point)
Responses
3
4
5
6
GPT 3.5
To find the length of ModifyingAbove upper M upper N with bar, we first need to find the coordinates of M and N.
The midpoint formula is given as:
midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Applying this formula to find the coordinates of M and N:
Coordinates of M:
M = ((1 + 9)/2, (5 + 7)/2)
M = (5, 6)
Coordinates of N:
N = ((9 + 7)/2, (7 + 13)/2)
N = (8, 10)
Now, we can use the distance formula to find the length of ModifyingAbove upper M upper N with bar:
d = √((x2-x1)^2 + (y2-y1)^2)
d = √((8-5)^2 + (10-6)^2)
d = √(3^2 + 4^2)
d = √(9 + 16)
d = √25
d = 5
Therefore, the length of ModifyingAbove upper M upper N with bar is 5.
The midpoint formula is given as:
midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Applying this formula to find the coordinates of M and N:
Coordinates of M:
M = ((1 + 9)/2, (5 + 7)/2)
M = (5, 6)
Coordinates of N:
N = ((9 + 7)/2, (7 + 13)/2)
N = (8, 10)
Now, we can use the distance formula to find the length of ModifyingAbove upper M upper N with bar:
d = √((x2-x1)^2 + (y2-y1)^2)
d = √((8-5)^2 + (10-6)^2)
d = √(3^2 + 4^2)
d = √(9 + 16)
d = √25
d = 5
Therefore, the length of ModifyingAbove upper M upper N with bar is 5.
no name
THANK YOU SO MUCH ALL OF THE ANSWERS ARE CORRECT FOR THE Midpoint and Distance in the Coordinate Plane QUICK CHECK
GPT 3.5
You're welcome! I'm glad I could help. If you have any more questions, feel free to ask.