Question

Question #6d8b6

Answer 1

Midpoint`=>` `"(1, 0)"`

Explanation:

The midpoint coordinates of a LINE which start (A = 1) and end (B = 2) points are:

`(x, y)_1`; `(x, y)_2` are defined by:

`((x_1+x_m)/2) = x_2; ((y_1+y_m)/2) = y_2`

`((-3+x_m)/2) = -1`

`((4+y_m)/2)= 2`

`"Finally"`

`=>` `(1, 0)_2`

Answer 2

`B=(1,0)`

Explanation:

`"there are 2 possible approaches"`

`color(blue)"Algebraic approach"`

`• "coordinates of midpoint "=1/2(x_A+x_B),1/2(y_A+y_B)`

`rArr(-3+x_B)/2=-1larrcolor(blue)"x-coord of midpoint"`

`rArr-3+x_B=-2`

`rArrx_B=-2+3=1`

`rArr(4+y_B)/2=2`

`rArr4+y_B=4`

`rArry_B=4-4=0`

`rArrB=(1,0)`

`color(blue)"Vector approach"`

`"since M is the midpoint of AB then"`

`vec(AM)=vec(MB)`

`rArrulm-ula=ulb-ulm`

`rArrulb=2ulm-ula`

`color(white)(rArrulb)=2((-1),(2))-((-3),(4))`

`color(white)(rArrulb)=((-2),(4))-((-3),(4))=((1),(0))`

`rArrB=(1,0)`