Answer:
The other endpoint
\((x_{2} , y_{2}) is (4,-3)\)
Step-by-step explanation:
Given
Point 1 (-2,3)
Midpoint = (1,0)
We're to calculate the other end point.
To solve this, we'll make use of the formula of midpoints of line
Given that two lines of coordinates \(P(x_{1} ,y_{1} )\) and \(Q(x_{2} ,y_{2} )\)
\((m_{1},m_{2}) = (\frac{(x_{1} + x_{2} )}{2} ,\frac{(y_{1} + y_{2} )}{2})\\Where\\m_{1} = \frac{(x_{1} + x_{2} )}{2} \\and\\m_{2} = \frac{(y_{1} + y_{2} )}{2})\\\)
From the question, we have
\(m_{1} = 1\\m_{2} = 0\\x_{1} = -2\\y_{1} = 3\\\)
Calculating \(x_{2}\)...
From \(m_{1} = \frac{(x_{1} + x_{2} )}{2}\)
By Substitution, we have
\(1 = \frac{-2+x_{2} }{2} \\2 = -2+x_{2}\\2 + 2 = x_{2}\\ x_{2} = 4\)
Calculating \(y_{2}\)...
From \(m_{2} = \frac{(y_{1} + y_{2} )}{2}\)
By Substitution, we have
\(0 = \frac{3+y_{2} }{2} \\0 = 3+y_{2}\\0 - 3 = y_{2}\\ y_{2} = -3\)
Hence, the other endpoint
\((x_{2} , y_{2}) is (4,-3)\)
