What is the measure of angle P 5cm 13cm 12cm

Given the set of vertices, determine whether parallelogram ABCD is a rhombus, rectangle or square. List all that apply. A(7,-4),

Sloan [31]

Given:

Vertices of a parallelogram ABCD are A(7,-4), B(-1,-4), C(-1,-12), D(7, -12).

To find:

Whether the parallelogram ABCD is a rhombus, rectangle or square.

Solution:

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using distance formula, we get

$AB=\sqrt{(-4-(-4))^2+(-1-7)^2}$

$AB=\sqrt{(-4+4)^2+(-8)^2}$

$AB=\sqrt{0+64}$

$AB=8$

Similarly,

$BC=\sqrt{(-1-(-1))^2+(12-(-4))^2}=8$

$CD=\sqrt{(7-(-1))^2+(-12-(-12))^2}=8$

$AD=\sqrt{(7-7)^2+(-12-(-4))^2}=8$

All sides of parallelogram are equal.

$AC=\sqrt{(-1-7)^2+(-12-(-4))^2}=8\sqrt{2}$

$BD=\sqrt{(7-(-1))^2+(-12-(-4))^2}=8\sqrt{2}$

Both diagonals are equal.

Since, all sides are equal and both diagonals are equal, therefore, the parallelogram ABCD is a square.

We know that, a square is special case of rectangles and rhombus.

So, parallelogram ABCD is a rhombus, rectangle or square. Therefore, the correct option is c.

7 0

3 years ago

How many solutions does 2.3y+3.2-y=2.1+1.3y+1.1 have?

jeka57 [31]

1.3y +3.2 = 1.3y +3.2

we notice that both sides of the equation are identical. So substitute y with any value and the equation would still be correct.

y has infinite solutions.

6 0

3 years ago

Karin has 461 songs downloaded joe has 123 more songs downloaded than Karin let s=the number of songs joe downloaded

Paul [167]

Answer:

s=461+123

Step-by-step explanation:

123 more is +125, and that's how many songs Joe, s, has.

4 0

3 years ago

Find the equation of a line through B(5,2) which is perpendicular to the line 3x+5=0. Hence find the coordinate of the foot of t

Oduvanchick [21]

Answer:

y=2, the equation of a line which is perpendicular to the line 3x+5=0

A(-5/3,2) the foot of the perpendicular from B to the line

Step-by-step explanation:

d1 : 3x+5=0, so 3x=-5, x=-5/3

y=2, the equation of a line which is perpendicular to the line 3x+5=0

A(-5/3,2) the foot of the perpendicular from B to the line

3 0

3 years ago

The sum of four times a number and five times another number is -28. The sum of nine times the first number and two times the se

Rina8888 [55]

Answer:

Step-by-step explanation:

$x,\ y-the\ numbers\\\\\text{The sum of four times a number and five times another number is -28:}\\\\4x+5y=-28\\\\\text{The sum of nine times the first number and two times the second number is 11:}\\\\9x+2y=11\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}4x+5y=-28&\text{multiply both sides by2}\\9x+2y=11&\text{multiply both sides by (-5)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}8x+10y=-56\\-45x-10y=-55\end{array}\right}\qquad\text{add both sides of the equation}$

$.\qquad-37x=-111\qquad\text{divide both sides by (-37)}\\.\qquad\qquad\boxed{x=3}\\\\\text{Put the value of x to the first equation:}\\\\4(3)+5y=-28\\12+5y=-28\qquad\text{subtrac 12 from both sides}\\5y=-40\qquad\text{divide both sides by 5}\\\boxed{y=-8}$

3 0

3 years ago