What is the endpoint of a line segment if the midpoint M( – 3, 4) and the other endpoint is E(7, – 2)? Answers
(– 13, 10)
(10, – 13)
(– 1, 2)
(2, – 1)

9514 1404 393

  (-13, 10)

Step-by-step explanation:

If M is the midpoint of segment DE, then ...

  D = 2M -E

  D = 2(-3, 4) -(7, -2) = (2(-3)-7, 2(4)+2) = (-13, 10)

The other end point is (-13, 10).

C.

yes, part c is completely independent of parts a and b.

they give you information about a point and the slope of a tangent line at that particular point. then they tell you to find the values of a and b.

since the derivative gives the tangent line slope, we can differentiate  with respect to , with   and   as constants.

my reasoning is this: notice how the formula for the derivative from part b was in terms of x and y. we do know that   and   and the value of the derivative (the slope) being , so if we differentiate, we might be able to solve for one of our constants.

note that  because   is a constant, not a function of . so if we differentiated, we could end up solving for .



our derivative has an unknown constant of a. but we can find this constant with our information.

the tangent line at point   has to have a slope of . substitute 1 for , 3 for , and   for .



to get the value of , use this value of a along with the given coordinates on the equation of the curve.



i confirmed my answer using a graphing calculator like desmos, attached. it seems like a reasonable tangent line.