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1 answer:
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Answer:
The other end point is: s+ti = 3+9i
Step-by-step explanation:
Mid-Point(M) in the complex plane states that the midpoint of the line segment joining two complex numbers a+bi and s+ti is the average of the numbers at the endpoints.
It is given by:
Given: The midpoint = -1 + i and the segment has an endpoint at -5 - 7i
Find the other endpoints.
Let a + bi = -5 -7i and let other endpoint s + ti (i represents imaginary )
Here, a = -5 and b = -7 to find s and t.
then;
[Apply Mid-point formula]
On comparing both sides
we get;
and
To solve for s:
or
-2 = -5+s
Add 5 to both side we have;
-2+5 = -5+s+5
Simplify:
3 = s or
s =3
Now, to solve for t;
2 =-7+t
Add 7 to both sides we get;
2+7 = -7+t+7
Simplify:
9 = t
or
t =9
Therefore, the other end point (s+ti) is, 3+9i
- Vertex Form:
, with (h,k) as the vertex.
So the new equation is in vertex form. And looking at this equation, we see the vertex as (-4,-7) <em>(Remember that y = (x + 4)^2 - 7 can be also written as y = (x - (-4))^2 - 7).</em>
Since negative x-coordinates go to the left on the x-axis and negative y-coordinates go down on the y-axis, <u>your answer is going to be C. It is the graph of y = x^2 translated 7 units down and 4 units to the left.</u>