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
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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.
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
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).
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
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.