Show that AC and BD bisect each other if A(–3, –5), B(2, –3), C(3, 5), and D(–2, 3). Find AC and BD

Step-by-step explanation:

midpoint of AC=((-3+3)/2,(-5+5)/2)=(0,0)

midpoint of BD=((2-2)/0,(-3+3)/2)=(0,0)

coordinates  of midpoint of AC and BD are same.

∴ AC and BD bisect each other.

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.