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mixer [17]
3 years ago
10

The coordinates of triangle FGH are F(2, 4), G(5, −9) and H(−3, −4). Which statement proves that triangle FGH is a right triangl

e? (m = y2 - y1 x2 - x1 )
Mathematics
2 answers:
Alecsey [184]3 years ago
3 0
The fact that the slopes of HF and GH are negative reciprocals proves that FGH is a right triangle.

The slope of HF is given by
m = (-4-4)/(-3-2) = -8/-5 = 8/5

The slope of GH is given by
m = (-4--9)/(-3-5) = (-4+9)/(-3-5) = 5/-8 = -5/8

These are reciprocals and opposite sides.  This only occurs if the lines are perpendicular; thus they make a right angle.
ArbitrLikvidat [17]3 years ago
3 0

The slope of GH= -5/8, and the slope of FH=8/5, therefore, GH | FH

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Explanation:
general form of the parabola is:
y = ax² + bx + c

Now, we will need to solve for a, b and c.
To do this, we will simply get points from the graph, substitute in the general equation and solve for the missing coefficients.

First point that we will use is (0,-3). 
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The equation now becomes:
y = ax² + bx - 3

The second point that we will use is (2,0):
y = ax² + bx - 3
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The third point that we will use is (-3,0):
y = ax² + bx - 3
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Substitute with I in II and solve for a as follows:
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Substitute with the value of a in equation I to get b as follows:
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Substitute with a and b in the equation as follows:
y = 0.5x² + 0.5x - 3

Hope this helps :)
7 0
3 years ago
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