$\left\begin{array}{ccc}A\left( \boxed{3} , \boxed{8} \right)&B\left( \boxed{9} , \boxed{6} \right )\\\\C\left( \boxed{1} , \boxed{4} \right)&D\left( \boxed{7} , \boxed{2} \right )\end{array}\right$

Step-by-step explanation:

The coordinates are:

$\left\begin{array}{ccc}A\left( \boxed{3} , \boxed{8} \right)&B\left( \boxed{9} , \boxed{6} \right )\\\\C\left( \boxed{1} , \boxed{4} \right)&D\left( \boxed{7} , \boxed{2} \right )\end{array}\right$

The parallelogram is attached below.

To verify if these coordinates form a parallelogram, we show that:

AB=CD; and
AC=BD

Using Distance Formula

$AB = \sqrt{(6-8)^2+(9-3)^2} = \sqrt{(-2)^2+(6)^2} = \sqrt{40} $ units$

$CD = \sqrt{(2-4)^2+(7-1)^2} = \sqrt{(-2)^2+(6)^2} = \sqrt{40} $ units$

$AC = \sqrt{(8-4)^2+(3-1)^2} = \sqrt{(4)^2+(2)^2} = \sqrt{20} $ units$

$BD = \sqrt{(6-2)^2+(9-7)^2} = \sqrt{(4)^2+(2)^2} = \sqrt{20} $ units$

Since AB=CD; and AC=BD, the coordinates A, B, C, and D form the vertex of a parallelogram.

3 0

3 years ago

What is the solution to this system of equations?

Rashid [163]

X=45
y=-8
check if this work

4 0

2 years ago

What is the simplest form of 4a + 8b/12<br> Step by step pls

shutvik [7]

Answer:

4a + 2b/3

Step-by-step explanation:

focus on 8b/12 first:

factor 8b/12 by 4 ---> 8b/12 = 4(2)b/4(3) ----> cancel 4 in the denominator and the nominator ---> 8b/12 = 4(2)b/4(3) = 2b/3

then, go back to 4a:

4a is in its simplest form, it can't be factor

therefore, plus 4a and 2b/3 = 4a + 2b/3

5 0

3 years ago

Find an explicit formula for the following sequence, an which starts with a1=2/3. 2/3,3/4,4/5,5/6,…

Flura [38]

Answer:

Step-by-step explanation:

a1=2/3

sequence is 2/3,3/4,4/5,...

for numerator a1=2

d=3-2=1

numerator of nth term=a1+(n-1)d=2+(n-1)×1=2+n-1=n+1

denominator = 1 more than numerator=n+1+1=n+2

so an=(n+1)/(n+2)

or for denominator a1=3,d=4-3=1

denominator of nth term=3+(n-1)×1=3+n-1=n+2

an=(n+1)/(n+2)

6 0

3 years ago