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finlep [7]
3 years ago
7

If (-2, -6) is the end point of the line segment and (3,0) is its midpoint , Find the other endpoint ?

Mathematics
1 answer:
Firlakuza [10]3 years ago
8 0

Answer:

(8, 6).

Step-by-step explanation:

Let the end-point be (x , y)

Then the midpoint ( using the endpoint ( -2, -6) )

= (x - 2)/2 , (y - 6)/2

But we are given that the midpoint is (3, 0), so:

(x - 2)/2 = 3

x - 2 = 6

x = 8  and

(y - 6) = 0

y = 6

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Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1.
Hitman42 [59]
(x-h)^2=4p(y-k)
we know it is this one because the directix is y=something and not x=something

(h,k) is the vertex
p is the distance from the vertex to the focus
it is 1/2 the distance from the vertex to the directix

if p is positive, the focus is above the vertex
if p is negative, the focus is below the vertex


we have
focus is (6,2) and directix is y=1
distance from (6,2) to y=1 is the distance from 2 to 1 which is 1
1/2=p
since 1<2, we see that the focus is above the vertex (when the focus is greater than the directix, then the graph opens to the right or up)

p=1/2
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vertex is (6,1.5)
p=1/2

(x-6)^2=4(0.5)(y-1.5)
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2nd option is answer
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