F the endpoints AB of have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of AB?
1 answer:
In these kind of problems, it's always the best to just draw it. There are "formulas" to calculate this, but it's better to know intuitively.
Midpoint, as the name suggests is the point that is exactly halfway between two points. To find a midpoint in one dimension, we would take an average between those two points.
Example: Number exactly halfway between 8 and 16 is
We can do the same for two dimensions, it just means we'll have to calculate both for x-values and y-values
Midpoint
Midpoint, as the name suggests is the point that is exactly halfway between two points. To find a midpoint in one dimension, we would take an average between those two points.
Example: Number exactly halfway between 8 and 16 is
We can do the same for two dimensions, it just means we'll have to calculate both for x-values and y-values
Midpoint
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The angle is 127°, so the Pythagorean theorem does not apply.
Generally, you would use the Law of Cosines to solve for the third side when given two sides and the angle between them.
EF^2 = 7^2 +15^2 -2*7*15*cos(127°)
EF ≈ √(400.3812) ≈ 20.00953
My guess is that you're expected to use 20 for the length of the 3rd side.
By Heron's formula, s = (7 +15 +20)/2 = 21
Area = √(21*(21 -7)*(21 -15)*(21 -20)) = √(21*14*6*1) = √1764 = 42 . . . . yd^2
_____
More directly,
.. Area = (1/2)*7*15*sin(127°) ≈ 41.928 . . . . yd^2
Generally, you would use the Law of Cosines to solve for the third side when given two sides and the angle between them.
EF^2 = 7^2 +15^2 -2*7*15*cos(127°)
EF ≈ √(400.3812) ≈ 20.00953
My guess is that you're expected to use 20 for the length of the 3rd side.
By Heron's formula, s = (7 +15 +20)/2 = 21
Area = √(21*(21 -7)*(21 -15)*(21 -20)) = √(21*14*6*1) = √1764 = 42 . . . . yd^2
_____
More directly,
.. Area = (1/2)*7*15*sin(127°) ≈ 41.928 . . . . yd^2