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The midpoint of AB is M(-4,-3). If the coordinates of A are (-1, -2), what arethe coordinates of B?

User Pochwar
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1 Answer

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If point M is in the midle of the line AB, this means that the distance from A to M is equal to the distance from M to B

Then AB= AM + MB

To calculate said distance you have to draw the points in the cartesian system.

By adding two lines paralell to the X-axis and the Y-axis you can create a right triangle where the line AM represents the hypothenuse. Using the pytagoras theorem you can use the length of the base and the height og the triangle to calculate the hypothenuse.

The base is parallel to the X-axis, so you have to use values of X to calculate its length:

b= XA-XM= -1-(-4)= -1+4= 3

The height is parallel to the Y-axis, so you have to use the values of Y to calculate its length:

h= YA-YM= -2-(-3)= -2+3=1

If AM=MB you can say that if you draw a triangle under MB, its base and heigth should have the same length. What you have to do to draw segment MB is mirror the triangle over the line corresponding to the value of Y= -3:

Once the second segment is drawn, you can read the coordinates of point B in it.

B(-7,-4)

The midpoint of AB is M(-4,-3). If the coordinates of A are (-1, -2), what arethe-example-1
The midpoint of AB is M(-4,-3). If the coordinates of A are (-1, -2), what arethe-example-2
User Ginalx
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