Answer:
The coordinates of the other point are:
(x₂, y₂) = (18, 20)
Hence, option A is correct.
Step-by-step explanation:
Given
- The midpoint (x, y) = (0, 5)
- The first point (x₁, y₁) = (-18, -10)
To determine
- The second point (x₂, y₂) = ?
Using the Mid-point formula between (x₁, y₁) and (x₂, y₂)
[tex]\left(x,\:y\right)=\:\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
Here:
(x, y) is the midpoint between (x₁, y₁) and (x₂, y₂)
substituting (x, y) = (0, 5) and (x₁, y₁) = (-18, -10) in the formula
[tex]\left(0,\:5\right)=\:\left(\frac{x_2+\left(-18\right)}{2},\:\:\frac{y_2+\left(-10\right)}{2}\right)[/tex]
equating
[tex]0=\frac{x_2+\left(-18\right)}{2}[/tex]
[tex]x_2-18=0[/tex]
Add 18 to both sides
[tex]x_2-18+18=0+18[/tex]
[tex]x_2=18[/tex]
also
[tex]5=\frac{y_2+\left(-10\right)}{2}[/tex]
[tex]10=y_2+\left(-10\right)[/tex]
[tex]10=y_2-10[/tex]
[tex]10+10=y_2[/tex]
[tex]10+10=y_2[/tex]
[tex]y_2=20[/tex]
Therefore, the coordinates of the other point are:
(x₂, y₂) = (18, 20)
Hence, option A is correct.
