Question

Y is the midpoint of XZ. X has coordinates (3, 4), and Y has coordinates (–1, 9). Find the coordinates of Z.

Answer 1

Answer:Z(-5,14)

Step-by-step explanation:Here, X (3,4) is a coordinate. And Y (-1,9) is a midpoint.

Let another endpoint of line be z(x,y)

We have,

Midpoint of XZ=((x1+x2)/2,(y1+y2)/2)

that is, (-1,9)=((3+x)/2,(4+y)/2)

Equating with their corresponding elements we get,

-1=((3+x)/2

-2=3+x

∴x=-5

Now,

Equation with their corresponding elements, We get,

9=((4+y)/2)

18=4+y

∴y=14

∴The coordinates of z are (-5,14).

Answer 2

Explanation:

Hey there!!

While finding the coordinates of any point, you remember to use formula first and then equate it.

So, let's begin to work accordingly.

Here, X (3,4) is a coordinate. And Y (-1,9) is a midpoint.

Let another endpoint of line be Z(x,y).

We have,

`midpoint \: of \: xz = ((x1 + x2)/(2) ,(y1 + y2)/(2)`)

Now,

`( - 1,9) = ((3 + x)/(2) ,(4 + y)/(2)`)

As they are equal, equating with their corresponding elements we get,

`- 1 = (3 + x)/(2)`

or, -2 = 3+x

Therefore, x= -5.

Now, again;

Equating with their corresponding elements we get,

`9 = (4 + y)/(2)`

or, 18 = 4+y

Therefore, y = 14.

Therefore, the coordinates of Z are (-5,14).

Hope it helps...