Question

Find the mid points of the line joining the pairs of points a.(3,4) and (5,2) b.(0,6) and (4,0) c.(4,2) and (4,-4) d.(-1,-5) and (-3,4) e.(-3,2) and (8,-2)

Answer 1

Answer:

a(4,3).  b( 2,3). c(4,-1). d(-2,-1/2).  e(5/2, 0).

Step-by-step explanation:

Hello , I can help you with that

the mid point is given by

Let

Point 1

$(x_{1},y_{1})$

Point 2

$(x_{2},y_{2})$

the midpoint is(m)

$m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )$

all you have to do is to put those values into the equation

Step 1

P1(3,4)  and P2(5,2)

$m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{3+5}{2},\frac{4+2}{2} )\\m=(\frac{8}{2},\frac{6}{2} )\\m=(4,3)$

Step 2

P1(0,6) and P2(4,0)

$m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{0+4}{2},\frac{6+0}{2} )\\m=(\frac{4}{2},\frac{6}{2} )\\m=(2,3)$

Step 3

P1(4,2) and P2(4,-4)

$m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{4+4}{2},\frac{2-4}{2} )\\m=(\frac{8}{2},\frac{-2}{2} )\\m=(4,-1)$

Step 4

P1(-1,-5) and P2(-3,4)

$m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{-1-3}{2},\frac{-5+4}{2} )\\m=(\frac{-4}{2},\frac{-1}{2} )\\m=(-2,\frac{-1}{2} )$

Step 5

P1(-3,2) and P2(8,-2)

$m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{-3+8}{2},\frac{2-2}{2} )\\m=(\frac{5}{2},\frac{0}{2} )\\m=(\frac{5}{2} ,0)$

I really hope it helps you, have a nice day