Question

What is the length of line AB with endpoints A(3,2) and B(8,14)

Answer 1

What is the midpoint of line AB with endpoints A(3,2) and B(8,14)

Answer 2

triangle ABC has verticies A(1,5) B(9,7) and C(7,13). M is the midpoint of AB and N is the midpoint of BC. WHich of the following is the length of MN

Answer 3

To find the length of line AB with endpoints A(3,2) and B(8,14), we can use the distance formula:

The distance formula is given by:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Using the given coordinates:
x1 = 3, y1 = 2
x2 = 8, y2 = 14

Substituting into the distance formula:
Distance = √((8 - 3)^2 + (14 - 2)^2)

Simplifying the equation:
Distance = √(5^2 + 12^2)
Distance = √(25 + 144)
Distance = √169
Distance = 13

Therefore, the length of line AB is 13 units.

Answer 4

To find the midpoint of line AB with endpoints A(3,2) and B(8,14), we can use the midpoint formula:

The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the given coordinates:
x1 = 3, y1 = 2
x2 = 8, y2 = 14

Substituting into the midpoint formula:
Midpoint = ( (3 + 8) / 2 , (2 + 14) / 2 )

Simplifying the equation:
Midpoint = ( 11 / 2 , 16 / 2 )
Midpoint = ( 5.5 , 8 )

Therefore, the midpoint of line AB is (5.5, 8).

Answer 5

To find the length of MN, we first need to find the coordinates of M and N.

Given that A(1,5), B(9,7), and C(7,13), we can calculate the coordinates of M and N using the midpoint formula:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

For M, the coordinates of A are (1,5) and the coordinates of B are (9,7).

Using the midpoint formula for M:
M = ( (1 + 9) / 2 , (5 + 7) / 2 )
M = ( 10 / 2 , 12 / 2 )
M = ( 5 , 6 )

For N, the coordinates of B are (9,7) and the coordinates of C are (7,13).

Using the midpoint formula for N:
N = ( (9 + 7) / 2 , (7 + 13) / 2 )
N = ( 16 / 2 , 20 / 2 )
N = ( 8 , 10 )

Now that we have the coordinates of M and N, we can find the length of MN using the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Using the given coordinates for M and N:
x1 = 5, y1 = 6
x2 = 8, y2 = 10

Distance = √((8 - 5)^2 + (10 - 6)^2)
Distance = √(3^2 + 4^2)
Distance = √(9 + 16)
Distance = √25
Distance = 5

Therefore, the length of MN is 5 units.