Question

the midpoint is AB is M(3,-2). One endpoint is A(7,-9). Find the coordinates of the other endpoint B.

Answer 1

To find the coordinates of the other endpoint B given the midpoint M and one endpoint A. Apply the midpoint formula and solve the equations to find the coordinates of B(-1, 5).

Step-by-step explanation:

The midpoint coordinates are given as M(3, -2) and one endpoint is given as A(7, -9). To find the coordinates of the other endpoint, we can use the midpoint formula which states that the coordinates of the midpoint are the average of the coordinates of the two endpoints.

Let the coordinates of the other endpoint be B(x, y). Using the midpoint formula, we have:

[(x + 7) / 2, (y + -9) / 2] = (3, -2)

Simplifying the equation, we get:

(x + 7) / 2 = 3

(y - 9) / 2 = -2

Multiplying both sides by 2, we have:

x + 7 = 6

y - 9 = -4

Subtracting 7 from both sides, we get:

x = -1

Subtracting -9 from both sides, we get:

y = 5

Therefore, the coordinates of the other endpoint are B(-1, 5).

Answer 2

The required points of the given line segment are ( - 1, - 5 ).

Step-by-step explanation:

Given that the line segment AB whose midpoint M is ( 3, -2 ) and point A is ( 7, - 9), then we have to find point B of the line segment AB -

As we know that-

If a line segment AB is with endpoints (
`x_(1), y_(1)` ) and (
`x_(2), y_(2)` )then the mid points M are-

M = (
`( x_(1) + x_(2) )/(2)` ,
`( y_(1) + y_(2)  )/(2)` )

Here,

Let A ( 7, - 9 ), B ( x, y ) with midpoint M ( 3, - 2 ) -

then by the midpoint formula M are-

( 3, - 2 ) = (
`( 7 + x)/(2)` ,
`( - 9 + y)/(2)` )

On comparing x coordinate and y coordinate -

We get,

(
`( 7 + x)/(2)` = 3 ,
`( - 9 + y)/(2)` = - 2)

( 7 + x = 6, - 9 + y = - 4 )

( x = 6 - 7, y = - 4 + 9 )

( x = - 1, y = -5 )

Hence the required points A are ( - 1, - 5 ).

We can also verify by putting these points into Midpoint formula.