Question

The midpoint of JK is point Lat (-1, 8). One endpoint is J(4.-15). Which equations can be solved to determine the coordinates

Answer 1

The options are: -2-4=x₁ and 15 + y₁=16.

Step-by-step explanation:

The formula for midpoint of a segment AB,where A(x,y) and B(x₁y₁) is given by;

(x+x₁)/2 , (y+y₁)/2

Given in question segment JK as J(4,-15) , midpoint of JK(-1,8) and K(x₁,y₁) then to find K(x₁,y₁) , apply the formula for mid point ;

(x+x₁)/2 , (y+y₁)/2

(-1,8) =(x₁+4)/2 , (y₁+ -15)/2

-1=(x₁+4)/2 ------------------multiply both sides by 2

-2=(x₁+4)

-2=x₁ +4 ---------------------collect like terms

-2-4=x₁

-6=x₁-------------------------The equation should be: -2-4=x₁

and

8= (y₁+ -15)/2

16= (y₁+ -15)

16=y₁+ -15

16+15=y₁

31=y₁------------------------15 + y₁=16

Checking the answers

Segment JK where J(4,-15) and K(-6,31) then the midpoint will be :

(x+x₁)/2 , (y+y₁)/2

(4+-6)/2 ,(-15+31)

(-2)/2 ,(16)/2

(-1,8) ---------midpoint of segment JK

Learn More

Midpoint of a segment formula : brainly.com/question/10424143

Finding midpoint of a segment :  brainly.com/question/7729444

Keyword : midpoint, endpoint,coordinates

#LearnwithBrainly

Answer 2

Answer:(1) -15+y1=16 and x2= 6 which is not present among the options

Step-by-step explanation:

We must first note that the midpoint of a line is given by,

x=(x1+x2)/2

and

y=( y1+y2)/2.

Since, the midpoint and point, J are on the same line, however , doing that is going to make the problem prove difficult,

Therefore,

We must note that the x coordinate of point K is just as far from the midpoint of the line as the x coordinate of J.

Therefore, 2x= Xj+Xk

Xk= 2(-1) - 4

Xk=-6

The same goes for Yk,

We must note that the y coordinate of point K is just as far from the midpoint of the line as the y coordinate of J.

Therefore, 2Y= Yj+Yk

Yk=2(8)-(-15)

Yk= 31

Therefore, the equation which satisfies Xk= 2, is the equation;

Probably, -(2+4)=X1

Which is not among the options

The equation which satisfies Yk=311, is the equation;

-15+y1=16.