Question

2. Label the coordinates as shown below.
c la b)
BO, b)
A
D
(a o
(c. O
a. Find the distance between A and C. Given: A (0, 0) and
C (a, b)
AC =
Va-02 + (6-0)
WARAN
Va? +02
AC =
C С
b. Find the distance between B and D.
c. Given: b (0, b)
and D (a, 0)
LYON
BD =
Va-0)' + (0-b)
BD - Va? +
Since AC = BD, then AC = BD by substitution.
Therefore, AC = BD. The diagonals of a rectangle are congruent.​

Answer 1

Answer:

Points “(a\quad +\quad b,\quad b\quad +\quad c)”and

(“a\quad -\quad b”,“c\quad -\quad b”)

To find:

“Distance between” the two pair.

Answer:

A (a+b, b+c) and B (a-b, c-d)

As per the given question

AB=\sqrt { ({ x }_{ 2 }-{ x }_{ 1 })^{ 2 }+({ y }_{ 2 }-{ y }_{ 1 })^{ 2 } }AB=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

We know that,

{ x }_{ 1 }\quad =\quad a\quad +\quad bx

1

=a+b

{ x }_{ 2 }\quad =\quad a\quad -\quad bx

2

=a−b

{ y }_{ 1 }\quad =\quad b\quad +\quad cy

1

=b+c

{ y }_{ 2 }\quad =\quad c\quad -\quad by

2

=c−b

\therefore AB=\sqrt{(a-b-a-b)^{2}+(c-b-b-c)^{2}}∴AB=

(a−b−a−b)

2

+(c−b−b−c)

2

=\sqrt{(-2 b)^{2}+(-2 b)^{2}}=

(−2b)

2

+(−2b)

2

=\sqrt{4 b^{2}+4 b^{2}}=

4b

2

+4b

2

=\sqrt{8 b^{2}}=

8b

2

AB=2 b \sqrt{2}AB=2b

2