Question

Find the coordinates of Z if Y is the midpoint of XZ , X( -10, 9) , and Y( -4,8)​

Answer 1

Answer: The required co-ordinates of Z are (2, 7).

Step-by-step explanation: Given that Y is the midpoint of XZ and the co-ordinates of X are (-10, 9) and the of Y are (-4, 8).

We are to find the co-ordinates of Z.

Let (a, b) represents the co-ordinates of the point Z.

We know that

the co-ordinates of the midpoint of a line segment with endpoints (x, y) and (z, w) are given by

`\left((x+z)/(2),(y+w)/(2)\right).`

So, according to the given information, we have

`\left((-10+a)/(2),(9+b)/(2)\right)=(-4,8)\\\\\\\Rightarrow (-10+a)/(2)=-4\\\\\Rightarrow -10+a=-8\\\\\Rightarrow a=-8+10\\\\\Rightarrow a=2`

and

`(9+b)/(2)=8\\\\\Rightarrow 9+b=16\\\\\Rightarrow b=16-9\\\\\Rightarrow b=7.`

Thus, the required co-ordinates of Z are (2, 7).

Answer 2

The coordinates of Z are (2,7)

Explanation:

we know that

The formula to calculate the midpoint between two points is equal to

`Y=((x1+x2)/(2) ,(y1+y2)/(2))`

we have

X(-10,9),Y(-4,8)

Let

(x2,y2) ----> the coordinates of Z

substitute the values

`(-4,8)=((-10+x2)/(2) ,(9+y2)/(2))`

Solve for x2

`-4=(-10+x2)/2\\-8=-10+x2\\x2=10-8\\x2=2`

Solve for y2

`8=(9+y2)/2\\16=9+y2\\y2=16-9\\y2=7`

therefore

The coordinates of Z are (2,7)