Question

VW has a midpoint at M(12, 0.5). Point V is at (10, -18). Find the coordinates of point W. Write the coordinates as decimals or integers.​

Answer 1

The coordinates of point W, which forms the line segment VW with midpoint M at (12, 0.5) and point V at (10, -18), are found to be (14, 19) through the midpoint formula.

Step-by-step explanation:

The midpoint M of a line segment VW on a Cartesian plane is the average of the coordinates of V and W. Since V is at (10, -18) and M is at (12, 0.5), we can find the coordinates of W by using the midpoint formula:

Midpoint M's x-coordinate = (Vx + Wx) / 2

Midpoint M's y-coordinate = (Vy + Wy) / 2

By substituting M's and V's coordinates into these equations, we can solve for W's coordinates:

12 = (10 + Wx) / 2

0.5 = (-18 + Wy) / 2

Solving these equations gives us W's x-coordinate and y-coordinate:

Wx = 2(12) - 10

Wy = 2(0.5) + 18

The completed calculations yield:

Wx = 14

Wy = 19

Therefore, the coordinates of point W are (14, 19).

Answer 2

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ V(\stackrel{x_1}{10}~,~\stackrel{y_1}{-18})\qquad W(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +10}{2}~~~ ,~~~ \cfrac{ y -18}{2} \right)~~ = ~~\stackrel{M}{(12~~,~~0.5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +10}{2}=12\implies x+10=24\implies \boxed{x=14} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -18}{2}=0.5\implies y-18=1\implies \boxed{y=19}`