Determine the equations of the following lines: (a) the line through (-1,3) and (2-4);(b) the line through (-1,2) and perpendicular to the line 2c-3y +5=0;(c) the line through (2,3) and the midpoint of the line segment from (-1,4) to (3,2)

Determine the equations of the following lines: (a) the line through (

1.	Determine the equations of the following lines: (a) the line through (-1,3) and (2-4);(b) the line through (-1,2) and perpendicular to the line 2c-3y +5=0;(c) the line through (2,3) and the midpoint of the line segment from (-1,4) to (3,2)
Answer» a)eq. of line through 2 points is(y-y1)=(y2-y1)/(x2-x1) (x-x1)y-3=(-4-3)/(2-(-1)) (x+1)y-3=-7/3 (x+1)3y-9=-7x-77x+3y=2b)eq. of line through 1 point isy=mx+cfor perpendicular lines product of slope is -1slope of given line is m1=2/3 let slope of required line be mthen m=-3/2y=-3x/2 +cputting point (-1,2)2=3/2 +cc=1/2soy=-3x/2 +1/22y+3x=1c)mid point of (-1,4) and (3,2) is(-1+3 /2,4+2 /2)=(1,3)required eq. from (2,3) and (1,3)(y-3)=(3-3)/(1-2) (x-1)y-3=0