What are the coordinates of the midpoint of HX if H(-1, 3) and X(7, -1)?
To find the midpoint of HX, we can use the midpoint formula. The midpoint formula states that the midpoint of a segment with endpoints (x1, y1) and (x2, y2) is given by the coordinates:
(midpoint_x, midpoint_y) = ((x1 + x2) / 2, (y1 + y2) / 2)
In this case, the coordinates of H are (-1, 3) and the coordinates of X are (7, -1).
Using the midpoint formula, we can calculate the midpoint coordinates as:
(midpoint_x, midpoint_y) = ((-1 + 7) / 2, (3 + -1) / 2)
= (6 / 2, 2 / 2)
= (3, 1)
Therefore, the coordinates of the midpoint of HX are (3, 1).
What is the length of AB with endpoints A(3, 2) and B(8, 14)?
To find the length of AB, we can use the distance formula. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of A are (3, 2) and the coordinates of B are (8, 14).
Using the distance formula, we can calculate the length of AB as:
distance = √((8 - 3)^2 + (14 - 2)^2)
= √(5^2 + 12^2)
= √(25 + 144)
= √169
= 13
Therefore, the length of AB is 13.
What is the midpoint of AB with endpoints A(3, 2) and B(8, 14)?
To find the midpoint of AB, we can use the midpoint formula. The midpoint formula states that the midpoint of a segment with endpoints (x1, y1) and (x2, y2) is given by the coordinates:
(midpoint_x, midpoint_y) = ((x1 + x2) / 2, (y1 + y2) / 2)
In this case, the coordinates of A are (3, 2) and the coordinates of B are (8, 14).
Using the midpoint formula, we can calculate the midpoint coordinates as:
(midpoint_x, midpoint_y) = ((3 + 8) / 2, (2 + 14) / 2)
= (11 / 2, 16 / 2)
= (5.5, 8)
Therefore, the midpoint of AB is (5.5, 8).
Triangle ABC has vertices A(1, 5), B(9, 7), and C(7, 13). M is the midpoint of AB and N is the midpoint of BC. What is the midpoint of MN?
To find the midpoint of MN, we need to find the coordinates of M and N first.
To find the coordinates of M, we can use the midpoint formula. The coordinates of A are (1, 5) and the coordinates of B are (9, 7).
Using the midpoint formula, we can calculate the coordinates of M as:
(midpoint_x, midpoint_y) = ((1 + 9) / 2, (5 + 7) / 2)
= (10 / 2, 12 / 2)
= (5, 6)
Therefore, the coordinates of M are (5, 6).
To find the coordinates of N, we can use the midpoint formula again. The coordinates of B are (9, 7) and the coordinates of C are (7, 13).
Using the midpoint formula, we can calculate the coordinates of N as:
(midpoint_x, midpoint_y) = ((9 + 7) / 2, (7 + 13) / 2)
= (16 / 2, 20 / 2)
= (8, 10)
Therefore, the coordinates of N are (8, 10).
Now, to find the midpoint of MN, we can use the midpoint formula once again. The coordinates of M are (5, 6) and the coordinates of N are (8, 10).
Using the midpoint formula, we can calculate the coordinates of the midpoint of MN as:
(midpoint_x, midpoint_y) = ((5 + 8) / 2, (6 + 10) / 2)
= (13 / 2, 16 / 2)
= (6.5, 8)
Therefore, the midpoint of MN is (6.5, 8).
thats not right
Apologies for the incorrect response. Let's recalculate the midpoint of MN using the correct coordinates.
We already calculated the coordinates of M as (5, 6). To find the coordinates of N, we need to use the midpoint formula again. The coordinates of B are (9, 7), and the coordinates of C are (7, 13).
Using the midpoint formula, we can calculate the coordinates of N as:
(midpoint_x, midpoint_y) = ((9 + 7) / 2, (7 + 13) / 2)
= (16 / 2, 20 / 2)
= (8, 10)
Therefore, the coordinates of N are (8, 10).
Now let's find the midpoint of MN. We have the coordinates of M as (5, 6), and the coordinates of N as (8, 10).
Using the midpoint formula, we can calculate the coordinates of the midpoint of MN as:
(midpoint_x, midpoint_y) = ((5 + 8) / 2, (6 + 10) / 2)
= (13 / 2, 16 / 2)
= (6.5, 8)
Therefore, the midpoint of MN is (6.5, 8).