How do we find the midpoint between (-a, -b, -c) and (3a, 3b, 3c)?

Answer 1

Mason Adams

The midpoint is

#(x_m,y_m)=((-a+3a)/2,(-b+3b)/2,(-c+3c)/2)=(a,b,c)#

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Answer 2

Sadie Allen

To find the midpoint between two points ( (x_1, y_1, z_1) ) and ( (x_2, y_2, z_2) ), you take the average of their coordinates:

Midpoint ( = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right) ).

Applying this formula to the given points ( (-a, -b, -c) ) and ( (3a, 3b, 3c) ), we get:

Midpoint ( = \left( \frac{-a + 3a}{2}, \frac{-b + 3b}{2}, \frac{-c + 3c}{2} \right) ).

Simplify each coordinate:

Midpoint ( = \left( \frac{2a}{2}, \frac{2b}{2}, \frac{2c}{2} \right) ).

Midpoint ( = (a, b, c) ).

So, the midpoint between ( (-a, -b, -c) ) and ( (3a, 3b, 3c) ) is ( (a, b, c) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.