Respuesta :
Answer:
B. [tex]B = (4,-2)[/tex]
Step-by-step explanation:
GIven that [tex]A = (-2, 2)[/tex] and [tex]M = (1, 0)[/tex], and that point M is the midpoint of AB, the midpoint can be determined as a vectorial sum of A and B. That is:
[tex]M = \frac{1}{2}\cdot A + \frac{1}{2}\cdot B[/tex]
The location of B is now determined after algebraic handling:
[tex]\frac{1}{2}\cdot B = M - \frac{1}{2}\cdot A[/tex]
[tex]B = 2\cdot M -A[/tex]
Then:
[tex]B = 2\cdot (1,0)-(-2,2)[/tex]
[tex]B = (2\cdot 1, 2\cdot 0)-(-2,2)[/tex]
[tex]B = (2,0) -(-2,2)[/tex]
[tex]B = (4,-2)[/tex]
Which corresponds to option B.
The coordinate of point B will be (4, -2). Then the correct option is B.
What is coordinate geometry?
Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Point A is located at (-2, 2), and point M is located at (1,0).
If point M is the midpoint of AB.
Then the location of point B will be
We know that the mid section formula
[tex]\rm (x, y) = \left ( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2} \right)[/tex]
Then the formula can be written as
x₂ = 2x - x₁ and y₂ = 2y - y₁
Then we have
x₂ = 2 × 1 + 2
x₂ = 4
y₂ = 2 × 0 - 2
y₂ = - 2
Then the coordinate of point B will be (4, -2).
Thus, the correct option is B.
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
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