Question #1aec1

Because #M# is the mid point of a straight line, the changes between the end point #J# and #M# must be the same as the changes between #M# and the end point #K#

The change in the #x# co-ordinate between #J# and #M# is #3 (8-5)#
Therefore the change in #x# from #M# to #K# must also be #3# so #K# has an #x# coordinate of #11 (8 + 3)#

The change in the #y# co-ordinate between #J# and #M# is #11 (5--6)#
Therefore the change in #y# from #M# to #K# must also be #11# so #K# has an #y# coordinate of #16 (5 + 11)#

#K# has co-ordinates of #(11, 16)#

#"2"#

#"questions of this type are best calculated using the"#

#color(blue)"Section formula"#

#"given a line segment say AB that has to be split in the"#
#"ratio m:n"#

#"if "A(x_1,y_1)" and "B(x_2,y_2)#

#"then the coordinates of the point splitting AB in ratio m:n"#
#"are found as follows"#

#•color(white)(x)[(mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)]#

#"here "(x_1,y_1)=(1,3)" and "(x_2,y_2)=(15,3)#

#"and "m:n=3:4#

#rArr(((3xx15)+(4xx1))/(3+4),((3xx3)+(4xx3))/(3+4))#

#=(49/7,21/7)=(7,3)to(B)#