Question

the midpoint m of segment Ab is located at the point (-2,1), in the standard x-y coordinate plane. if segment Ab has the length of 10 units and point A is located at (3,1) what are the coordinates of point b?​

Answer 1

SOLUTION

GIVEN

• The midpoint M of segment AB is located at the point (-2,1 ) in the standard xy coordinate plane.

• The segment AB has the length of 10 units

• The point A is located at (3,1)

TO DETERMINE

The coordinates of point B

EVALUATION

The midpoint M of segment AB is located at the point (-2,1 ) in the standard xy coordinate plane.

The point A is located at (3,1)

Let (x, y) be the coordinates of the point B

Then the mid point M of the line AB is

$= \displaystyle \sf{ \bigg( \frac{x + 3}{2} \: , \frac{y + 1}{2} \bigg) }$

Again it is given that Midpoint M is (-2,1)

So

$\displaystyle \sf{ \frac{x + 3}{2} = - 2 \: }$

$\implies \displaystyle \sf{ {x + 3} = - 4 \: }$

$\implies \displaystyle \sf{ x = - 7 \: }$

Also

$\displaystyle \sf{ \frac{y + 1}{2} = 1 \: }$

$\implies \displaystyle \sf{ y + 1 = 2\: }$

$\implies \displaystyle \sf{y = 1 \: }$

So the coordinates of the required point B is (-7,1)

CHECK

It can also be checked that the distance between A and B is

$= \sf{ \sqrt{ {(3 + 7)}^{2} + {(1 - 1)}^{2} } \: } \: \: \: unit$

$= \sf{ \sqrt{100 + 0} } \: \: \: \: unit$

$\sf{ = 10 \: \: \: unit \: }$

FINAL ANSWER

The coordinates of the required

point B is (-7 ,1 )

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

Find the equation of straight line passing through the point (-4,5) and making equal intercepts on the coordinate axis.

https://brainly.in/question/25257443

Answer 2

Answer:

Step-by-step explanation:

cgsxhtfhefkycdkyjrjtdyf