Eghit feet less than twice the width translate the exxpression from verbal to algabraic
2 answers:
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Answer:
Yes, the right angle is angle C.
Step-by-step explanation:
The given triangle has vertices at A(–2, 3), B(–3, –6), and C(2, –1).
Recall the slope formula;
The slope of the line going through AC is
The slope of the line going through BC s
The product of the slopes of AC and BC is
This means line AC is perpendicular to BC at C.
Hence the triangle ABC is right angled at C.
Answer:
(x²-10x+33)/(-8) = y
Step-by-step explanation:
The distance between any point on a parabola from both its focus and directrix are the same.
Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,
is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.
Equating the two equations given, we have
square both sides to get
(x-5)²+(y+3)²=(y-1)²
expand the y components
(x-5)² + y²+6y+9 = y²-2y+1
subtract y²+6y+9 from both sides
(x-5)² = -8y - 8
expand the x components
x²-10x+25 = -8y - 8
add 8 to both sides to isolate the -8y
x²-10x+33 = -8y
divide both sides by -8 to isolate y
(x²-10x+33)/(-8) = y