Question

How to find endpoint? please give good explanation ​

Answer 1

• Let other endpoint be (x2,y2)
• One endpoint(5,10)
• Midpoint(-3,-3)

Using midpoint formula

`\boxed{\sf (x,y)=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)}`

`\\ \rm\longmapsto (-3,-3)=\left((5+x_2)/(2),(10+y_2)/(2)\right)`

Firstly

`\\ \rm\longmapsto (5+x_2)/(2)=-3`

`\\ \rm\longmapsto 5+x_2=2(-3)=-6`

`\\ \rm\longmapsto x_2=-6-5`

`\\ \rm\longmapsto x_2=-11`

Now

.
`\\ \rm\longmapsto (10+y_2)/(2)=-3`

`\\ \rm\longmapsto 10+y_2==2(-3)`

`\\ \rm\longmapsto 10+y_2=-6`

`\\ \rm\longmapsto y_2=-6-10`

`\\ \rm\longmapsto y_2=-16`

Hence the coordinates are

• (x2,y2=(-11,-16)

Answer 2

(-11 , -16)

Explanation:

The midpoint will always be, as the term suggests, in the middle of the line segment. You simply need to find the distance for both x & y, and to apply that to the midpoint. In this case:

Endpoint (x₁ , y₁): (5 , 10)

Midpoint (x₂ , y₂): (-3 , -3)

Note that when finding distance, you will subtract the point₂ from point₁:

x: 5 - (-3) = 8

y: 10 - (-3) = 13

Therefore, each time you plot another point, you will be subtracting 8 from the x value, and 13 from the y value:

Endpoint (x₃ , y₃) = Midpoint (-3 , -3) + (_ - 8 , _ - 13) = (-11 , -16)

(-11 , -16) is your answer.

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