# Q,R and S are point on the line joining the point P and T. #P(a,x), T(b,y)# such that #TQ=QR=RS=SP#. Then the co-ordinates #((5a + 3b)/8,(5x+3y)/8)# is the mid-point of which segment?

##### 1 Answer

Sep 20, 2017

#### Explanation:

#"using the "color(blue)"section formula"#

#"given a line sectioned in the ratio m:n "#

#"then the coordinates of a point are"#

#((mx_1+nx_2)/(m+n)),((my_1+ny_2)/(m+n))#

#"here "m:n=5:3#

#"the section is therefore "#

#"T to mid-point of RS: mid-point of RS to P"#

#="ratio "5:3#

#(x_1,y_1)=(a,x)" and "(x_2,y_2)=(b,y)#

#rArr((5a+3b)/8,(5x+3y)/8)#