Which expression is equivalent to the expression 6h + 2?
2 answers:
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Answer:
(A) see below
(B) the right angle is at vertex B(-4,11)
(1) 3x -4y = -46
(E) the midpoint is (-4, 8.5)
Step-by-step explanation:
(A) The slope of line AB is Δy/Δx = (11-7)/(-4-(-6)) = 4/2 = 2. The slope of line BC is (10-11)/(-2-(-4)) = -1/2. The slopes of AB and BC have a product of 2(-1/2) = -1, so are the slopes of perpendicular lines. The points are distinct, and lines joining two pairs of them are at right angles, so the points form a right triangle.
(B) Point B(-4,11) is the point of intersection of perpendicular segments AB and BC, so is the location of the right angle.
(1) The slope of the hypotenuse AC is ...
Δy/Δx = (10-7)/(-2-(-6)) = 3/4
In point-slope form, the equation for the line through point A with this slope is ...
y -7 = 3/4(x +6) . . . . point-slope form of the equation of the hypotenuse
4y -28 = 3x +18 . . . . multiply by 4
-46 = 3x -4y . . . . . . subtract 18+4y
3x -4y = -46 . . . . . . . standard form equation of the hypotenuse
(E) The midpoint of the hypotenuse is the average of the endpoint coordinates:
M = (A + C)/2 = (-6-2, 7+10)/2 = (-4, 8.5)
The midpoint of the hypotenuse is M(-4, 8.5).
A decimal number with a digit (or group of digits) that repeats forever. The part that repeats can also be shown by placing dots over the first and last digits of the repeating pattern, or by a line over the pattern. Also called a "Repeating Decimal".
