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Determine the coordinates of the midpoint of the line segment joining the points (a) $(9,11)$ and $(16,-28),(b)(-5,13)$ and $(2,-19).$

(a) $(25 / 2,-17 / 2)$(b) $(-3 / 2,-3)$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 9

Elements of Geometry

Derivatives

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04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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Determine the coordinates …

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Find the coordinates of th…

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Find the midpoint of the l…

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Find the distance between …

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for this problem. We've been asked to find the midpoint of two different line segments. Each line segment we have the endpoints for. How can we use those to find the midpoint? Well, let's do just a sample picture. This is not one of our two cases. This is just a generic line. Let's say I have two points and I have the line connecting them. But by visual inspection, the midpoint is going to be somewhere about there. What does that look like when I'm looking at the endpoints? First let's look at X is for my first point. My X coordinate is here. The second one is here. So going from point A to point B, I'm traveling this far along my X axis. Well, by mid point is going to be the halfway point between those two. The number halfway between two other points is the average. So the X coordinate of my mid point is the average of the excess of my endpoints of the line segment. The same thing happens with wise point. A has a Y coordinate here. Point B is about there, so that's the distance between them and the Y. Coordinate in my mid point is about the halfway point. So for the y coordinate, I want to average my wise of the two end points. So let's try to use that for our line segments here for X coordinate. We want to average our exes, so that's gonna be nine plus 16 divided by two. Now we average are wise 11 plus negative, 28/2. And doing this out gives me 25 halves and negative 17 halves. How about our second line with segment again average The X is negative five plus 2/2, and I average my wise 13 plus negative 19 over to, which gives me values of negative three halves and negative three. So these are the two mid points for our two line segments.

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