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

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

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=((x_(1)+x_(2))/(2),(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=((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2) )\\m=((3+5)/(2),(4+2)/(2) )\\m=((8)/(2),(6)/(2) )\\m=(4,3)`

Step 2

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

`m=((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2) )\\m=((0+4)/(2),(6+0)/(2) )\\m=((4)/(2),(6)/(2) )\\m=(2,3)`

Step 3

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

`m=((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2) )\\m=((4+4)/(2),(2-4)/(2) )\\m=((8)/(2),(-2)/(2) )\\m=(4,-1)`

Step 4

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

`m=((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2) )\\m=((-1-3)/(2),(-5+4)/(2) )\\m=((-4)/(2),(-1)/(2) )\\m=(-2,(-1)/(2) )`

Step 5

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

`m=((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2) )\\m=((-3+8)/(2),(2-2)/(2) )\\m=((5)/(2),(0)/(2) )\\m=((5)/(2) ,0)`

I really hope it helps you, have a nice day