AB has endpoints A(-3,2) and B (3,-2)
Find the coordinates of the midpoint of AB
Find AB to the nearest tenth.
A ( - 3 , 2 ) mean :
xA = - 3
yA = 2
B ( 3 , - 2 ) mean :
xB = 3
yB = 2
x- coordinate of midpoint :
xmid = ( xB + xA ) / 2
xmid = ( - 3 + 3 ) / 2 = 0
y- coordinate of midpoint :
ymid = ( yB + yA ) / 2
ymid = ( - 2 + 2 ) / 2 = 0
Coordinates of the midpoint : ( 0 , 0 )
AB = sqrt [ ( xB - xA ) ^ 2 + ( yB - yA ) ^ 2 ]
AB = sqrt [ ( 3 - ( - 3 ) ) ^ 2 + ( - 2 - 2 ) ^ 2 ]
AB = sqrt [ ( 3 + 3) ) ^ 2 + ( - 2 - 2 ) ^ 2 ]
AB = sqrt [ 6 ^ 2 + ( - 4 ) ^ 2 ]
AB = sqrt ( 36 + 16 )
AB = sqrt ( 52 )
AB = 7.2111
AB = 7.2
to the nearest tenth
Oh, midpoint, the center of attention! Let me calculate that for you. To find the midpoint, we can simply average the x-coordinates and y-coordinates of the endpoints. So, let's do some math.
The x-coordinate of the midpoint can be found by averaging the x-coordinates of A and B: (-3 + 3) / 2 = 0 / 2 = 0.
Similarly, the y-coordinate of the midpoint can be found by averaging the y-coordinates of A and B: (2 + -2) / 2 = 0 / 2 = 0.
Therefore, the coordinates of the midpoint are (0, 0). Voila!
Now, for the second part of your question, let's calculate the distance AB. Using the distance formula, we have:
AB = sqrt((3 - (-3))^2 + (-2 - 2)^2)
= sqrt(6^2 + (-4)^2)
= sqrt(36 + 16)
= sqrt(52)
≈ 7.2 (rounded to the nearest tenth).
So, the coordinates of the midpoint are (0, 0) and the distance AB is approximately 7.2 units. Hope that brings a smile to your face!
To find the coordinates of the midpoint of AB, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by the coordinates ((x₁ + x₂)/2, (y₁ + y₂)/2).
Given that A has coordinates A(-3,2) and B has coordinates B(3,-2), we can apply the formula to find the midpoint of AB.
For the x-coordinate: (x₁ + x₂)/2 = (-3 + 3)/2 = 0/2 = 0
For the y-coordinate: (y₁ + y₂)/2 = (2 + (-2))/2 = 0/2 = 0
Therefore, the coordinates of the midpoint of AB are (0, 0).
To find the length of AB, we can use the distance formula, which states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula √((x₂ - x₁)² + (y₂ - y₁)²).
Given that A has coordinates A(-3,2) and B has coordinates B(3,-2), we can apply the formula to find the length of AB.
Distance = √((3 - (-3))² + (-2 - 2)²)
= √((6)² + (-4)²)
= √(36 + 16)
= √52
≈ 7.2 (rounded to the nearest tenth)
Therefore, the length of AB, to the nearest tenth, is approximately 7.2.
To find the coordinates of the midpoint of AB, we need to average the x-coordinates and the y-coordinates of the endpoints A and B.
The x-coordinate of the midpoint is the average of the x-coordinates of A and B. So, we add the x-coordinates -3 and 3 and divide the sum by 2:
(-3 + 3)/2 = 0/2 = 0
The y-coordinate of the midpoint is the average of the y-coordinates of A and B. So, we add the y-coordinates 2 and -2 and divide the sum by 2:
(2 + (-2))/2 = 0/2 = 0
Therefore, the coordinates of the midpoint of AB are (0, 0).
To find the length of AB to the nearest tenth, we can use the distance formula, which states:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates of A(-3, 2) and B(3, -2), we have:
d = sqrt((3 - (-3))^2 + (-2 - 2)^2)
d = sqrt(6^2 + (-4)^2)
d = sqrt(36 + 16)
d = sqrt(52)
To find the length to the nearest tenth, we calculate the square root of 52:
d ≈ sqrt(52) ≈ 7.211
Therefore, the length of AB to the nearest tenth is approximately 7.2.