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The midpoint of segment AB is (−10, 3). If A is located at (2, −4), what is the location of B? Explain your reasoning.

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Final answer:

By using the midpoint formula, we can deduce that the coordinates of point B are (-22, 10), as it is the endpoint opposite to A of the segment AB with a given midpoint.

Step-by-step explanation:

To find the location of point B, we utilize the concept of the midpoint in coordinate geometry. The midpoint formula states that the midpoint M(x,y) of a segment with endpoints A(x1, y1) and B(x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2). Since we know that M is at (-10, 3) and A is at (2, -4), we can set up the following equations to solve for B's coordinates:

M_x = (A_x + B_x)/2 \\ M_y = (A_y + B_y)/2

Substituting the given values leads to:

(-10) = (2 + B_x)/2

3 = (-4 + B_y)/2

By solving these equations, we find that:

  • B_x = -10 * 2 - 2 = -22
  • B_y = 3 * 2 + 4 = 10

Therefore, the coordinates of point B are (-22, 10).

User Dasmikko
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