Question #6d8b6

2 Answers
Jan 25, 2018

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#

Jan 25, 2018

#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)#