The midpoint of heat segment ab is (2, -5). If the collaborates of point A are (4, 4), what space the collaborates of B?

Explanation:

The fastest method to discover the absent endpoint is to determine the distance from the well-known endpoint to the midpoint and then performing the same revolution on the midpoint. In this case, the x-coordinate move from 4 come 2, or down by 2, so the brand-new x-coordinate have to be 2-2 = 0. The y-coordinate move from 4 to -5, or under by 9, so the new y-coordinate have to be -5-9 = -14.

You are watching: If the endpoints of have the coordinates a(9, 8) and b(-1, -2), what is the midpoint of ?

An alternate solution would be to substitute (4,4) because that (x1,y1) and (2,-5) for (x,y) into the midpoint formula:

x=(x1+x2)/2

y=(y1+y2)/2

Solving each equation for (x2,y2) returns the equipment (0,-14).

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### Example question #2 : just how To uncover The Endpoints that A heat Segment

Point A is (5, 7). Allude B is (x, y). The midpoint of ab is (17, –4). What is the value of B?

**Possible Answers:**

(22, –9)

(12, –11)

None the the other answers

(8.5, –2)

(29, –15)

**Correct answer:**

(29, –15)

Explanation:

Point A is (5, 7). Allude B is (x, y). The midpoint of abdominal muscle is (17, –4). What is the value of B?

We have to use our generalized midpoint formula:

MP = ( (5 + x)/2, (7 + y)/2 )

Solve each separately:

(5 + x)/2 = 17 → 5 + x = 34 → x = 29

(7 + y)/2 = –4 → 7 + y = –8 → y = –15

Therefore, B is (29, –15).

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### Example concern #3 : just how To discover The Endpoints the A line Segment

Line segment abdominal muscle has an endpoint, A, located at

, and also a midpoint at . What are the coordinates for suggest B that segment AB?**Possible Answers:**

The 2nd endpoint cannot exist

**Correct answer:**

Explanation:

With one endpoint A situated at (10,-1), and also a midpoint in ~ (10,0), we desire to add the length from A come the midpoint onto the various other side that the segment to find suggest B. The full length that the segment have to be double the street from A to the midpoint.

A is located precisely one unit listed below the midpoint follow me the y-axis, because that a full displacement that (0,1). To find suggest B, we add (10+0, 0+1), and get the coordinates for B: (10,1).

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### Example concern #4 : just how To find The Endpoints of A line Segment

Solve every problem and decide i beg your pardon is the best of the choices given.

What is the distance between the clues

and on a conventional coordinate plane?**Possible Answers:**

**Correct answer:**

Explanation:

Make a triangle. The points space 8 units apart top top the

-axis, and also units apart on the -axis. Then use the Pythagorean organize to discover the distance of the hypotenuse, which ends up being .Another means to resolve this problem is to usage the street formula,

Plugging in the 2 points us get,

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