Question

What’s the midpoint

Answer 1

The formula of a midpoint of HX:

`M\left((x_H+x_X)/(2),\ (y_H+y_X)/(2)\right)`

We have the points

`H\left(4(1)/(2),\ -4\deac{3}{4}\right),\ X\left(2\deac{1}{4},\ -2(3)/(4)\right)`

Substitute:

`x_M=(4(1)/(2)+2(1)/(4))/(2)=(4(1\cdot2)/(2\cdot2)+2(1)/(4))/(2)=(4(2)/(4)+2(1)/(4))/(2)=((4+2)+(2+1)/(4))/(2)\\\\=(6(3)/(4))/(2)=6(3)/(4):2=(6\cdot4+3)/(4)\cdot(1)/(2)=(27)/(4\cdot2)=(27)/(8)=3(3)/(8)\\\\y_M=(-4(3)/(4)+\left(-2(3)/(4)\right))/(2)=(-(4+2)-(3+3)/(4))/(2)=(-6(6)/(4))/(2)=-6(3)/(2):2\\\\=-(6\cdot2+3)/(2)\cdot(1)/(2)=-(15)/(4)=-3(3)/(4)`

Answer:
`M\left(3\deac{3}{8},\ -3(3)/(4)\right)`