The vertices of quadrilateral abcd are a(1, a - 3), b(10, a), c(9, a + 3) and d(0, a).prove that the quadrilateral is a rectangle. find the midpoints of the diagonals. the midpoint of ac is (5,1)the midpoint of bd is (5,1)find the lengths of the diagonals.

Answer with explanation:

The Vertices of quadrilateral A B CD, are A(1, a - 3), B(10, a), C(9, a + 3) and D(0, a).

Mid point of AC= (5,1)

Mid point of B D= (5,1)

Mid point formula of two points having coordinates , (a,b) and (c,d) is , if (x,y), then

So, the coordinates of vertices of quadrilateral A B CD, are A(1, -2), B(10, 1), C(9, 4) and D(0, 1).

Distance formula of two points having coordinates, (a,b) and (c,d) is,

Opposite sides  AB and CD are equal to 3√10 unit and , BC and AD are equal to √10 unit.

Also,length of Diagonals , AC=B D=10 unit.

∴ The Quadrilateral, AB CD is a Rectangle.

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!

do you have a picture of the table