All categories

2 years ago

The quadrilateral shown is rotated 90° clockwise about the origin. In which quadrant is the image of the quadrilateral located?

Mathematics

1 answer:

Viktor [21]2 years ago

4 0

Answer:

Option (2). 1

Step-by-step explanation:

Coordinates of point A, B, C and D are,

A(-4, 4), B(-2, 4), C(-2, 1) and D(-4, 3).

Quadrilateral ABCD when rotated 90° clockwise about the origin,

Rule for the rotation of the vertices,

(x, y) → (y, -x)

Following the rule of rotation coordinates of the image points,

A(-4, 4) → A'(4, 4)

B(-2, 4) → B'(4, 2)

C(-2, 1) → C'(1, 2)

D(-4, 3) → D'(3, 4)

Since all image points have the positive coordinates (x and y coordinates), image quadrilateral A'B'C'D' will be located in 1st quadrant.

Option (2) is the correct option.

You might be interested in

the area of a rectangle is 90 in2^. the ratio of the length to the width is 5:2. find the length and the width

-BARSIC- [3]

Length and width of rectangle is 15 inches and 6 inches respectively

<h3><u>Solution:</u></h3>

Given that area of a rectangle is 90 square inch

Ratio of length to the width = 5: 2.

Need to determine length and width of rectangle.

As ratio of length to the width is 5 : 2

Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.

<em><u>The formula for area of rectangle is given as:</u></em>

$\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}$

Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:

$\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}$

On solving the above expression for x we get

$\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}$

$\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}$

Hence length and width of rectangle is 15 inches and 6 inches.

4 0

3 years ago

Ten members of the academic team went to a local restaurant after their contest. Each meal combo that came with soda cost $6.75,

Aneli [31]

Answer:

7 ordered with Soda;

3 ordered with water

Step-by-step explanation:

Given

$m \to$ With water

$n \to$ With Soda

So:

$m + n =10$ --- total

$5m + 6.75n = 62.25$ -- cost

Required

Find m and n

$m + n =10$

Make m the subject

$m = 10 - n$

Substitute $m = 10 - n$ in $5m + 6.75n = 62.25$

$5(10-n) +6.75n = 62.25$

$50-5n +6.75n = 62.25$

Collect like terms

$-5n +6.75n = 62.25 - 50$

$-5n +6.75n = 12.25$

$1.75n = 12.25$

Solve for n

$n = 12.25/1.75$

$n = 7$

$m = 10 - n$

$m = 10 - 7$

$m =3$

8 0

3 years ago

The sum of the squares of two consecutive even integers is 884. determine the integers.

Digiron [165]

Answer:

(2x+1)(1) = 84. 2x+1= 84. 2x = 83.

Step-by-step explanation:

5 0

2 years ago

A quadrilateral is dilated by a scale factor of 2. It's original side measures are 7, 14, 21, and 28.

algol13

Answer:

14,28,42 and 56

Step-by-step explanation:

Multiply all lengths by 2 as the quadrilateral is dilated by a scale factor of 2

6 0

2 years ago

Read 2 more answers

~PLEASE HELP ASAP OFFERING 10 POINTS~

Marina CMI [18]

T = c + cb
t - c = cb
(t - c)/c = b
b = (t - c)/c

6 0

3 years ago