The mid-point of the straight line joining A(4,-3), B(6,-2) is located at C.
(a) Calculate the coordinates of C.
(b) Verify your result by calculating the distances AC and BC and showing they are equal.
I HAVE COMPLETED A BUT CAN'T DO DO B!!!!
try to use distance formula, then compare their distance
Do I have to do part a too ?
-2 + -3 = -5
-5/2 = -2.5 which is y of C
4 ) 6 = 10
10/5 = 5 which is x of C
so
C(5, -2.5)
now AC
dx = 5-4 = 1
dy = -2.5 - -3 = .5
d^2 = 1+.25
now CB
dx = 6 -5 = 1
dy = -2 - -2.5 = .5
d^2 = 1 + .25 the same
To calculate the distances AC and BC, we first need to find the coordinates of point C, which is the midpoint of the line segment AB.
To find the coordinates of the midpoint, we use the midpoint formula:
Midpoint (Cx, Cy) = ((Ax + Bx) / 2, (Ay + By) / 2)
Using this formula, let's calculate the coordinates of point C:
(a) Calculate the coordinates of C:
Given points:
A(4, -3)
B(6, -2)
Using the midpoint formula:
Cx = (4 + 6) / 2
Cx = 10 / 2
Cx = 5
Cy = (-3 + -2) / 2
Cy = -5 / 2
Cy = -2.5
Therefore, the coordinates of point C are C(5, -2.5).
(b) Verify the result by calculating the distances AC and BC:
To calculate the distance between two points, we use the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Let's calculate the distances AC and BC:
AC:
x₁ = 4, y₁ = -3 (coordinate of A)
x₂ = 5, y₂ = -2.5 (coordinate of C)
Distance AC = √((5 - 4)² + (-2.5 - (-3))²)
= √(1² + 0.5²)
= √(1 + 0.25)
= √1.25
BC:
x₁ = 6, y₁ = -2 (coordinate of B)
x₂ = 5, y₂ = -2.5 (coordinate of C)
Distance BC = √((5 - 6)² + (-2.5 - (-2))²)
= √((-1)² + (-0.5)²)
= √(1 + 0.25)
= √1.25
Both distances AC and BC are equal to √1.25, which shows that the result is correct.
Therefore, the distances AC and BC are equal, confirming the midpoint C(5, -2.5) is correct.