sat Math help » Geometry » name: coordinates Geometry » currently » Midpoint Formula » just how to discover the endpoints that a line segment

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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