Given the point m(-3,-4) is the midpoint of XY and that X(7,4)answer the following ;
A Find the coordinates of Y .
B Find the distance between X and Y ?
A. (17,12)
B. d = √(20² + 16²)
To find the coordinates of point Y, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint, M, of a line segment with endpoints (x₁, y₁) and (x₂, y₂) can be found by taking the average of the x-coordinates and the y-coordinates:
x-coordinate of M = (x₁ + x₂) / 2
y-coordinate of M = (y₁ + y₂) / 2
In this case, we have the coordinates of the midpoint M(-3, -4), and one endpoint X(7, 4). Let's denote the coordinate of point Y as (x, y). Using the midpoint formula, we can write:
-3 = (7 + x) / 2
-4 = (4 + y) / 2
To find the coordinates of point Y, we can solve this system of equations. Let's solve the first equation for x:
-3 = (7 + x) / 2
Multiply both sides by 2: -6 = 7 + x
Subtract 7 from both sides: -13 = x
Now let's solve the second equation for y:
-4 = (4 + y) / 2
Multiply both sides by 2: -8 = 4 + y
Subtract 4 from both sides: -12 = y
Therefore, the coordinates of point Y are (-13, -12).
To find the distance between points X and Y, we can use the distance formula. The distance formula states that the distance d between two points (x₁, y₁) and (x₂, y₂) can be calculated using the following formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, we have the coordinates of point X (7, 4) and point Y (-13, -12). Substituting these values into the distance formula, we get:
d = √((-13 - 7)² + (-12 - 4)²)
= √((-20)² + (-16)²)
= √(400 + 256)
= √656
≈ 25.6
Therefore, the distance between points X and Y is approximately 25.6 units.