Question

basic formulas and linear equations quiz
the point (3, -4) is the midpoint of the line segment in the standard (x, y) coordinate plane joining the point (8, -11) and the point (a, b). which of the following is (a, b)?
o (-2, 3)
o (-2, 19)
o (2, -3)
o (2.5, -3.5)
o (5.5, -7.5)

Explanation:

Step1: Use mid - point formula for x - coordinate

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).
For the x - coordinate: \(\frac{8 + a}{2}=3\).
Multiply both sides by 2: \(8 + a=6\).
Subtract 8 from both sides: \(a=6 - 8=-2\).

Step2: Use mid - point formula for y - coordinate

For the y - coordinate: \(\frac{-11 + b}{2}=-4\).
Multiply both sides by 2: \(-11 + b=-8\).
Add 11 to both sides: \(b=-8 + 11 = 3\).

Answer:

\((-2,3)\)