Rectangle qrst has coordinates q ( − 3 , 7 ) , r ( − 3 , 11 ) , s ( 4 , 11 ) , and t ( 4 , 7 ) . dilate the rectangle by a scale factor of 3 with a center of dilation at the origin. what are the coordinates of rectangle q 'r 's 't '? explain your reasoning. q ' ( , ) r ' ( , ) s ' ( , ) t ' ( , ) is the dilation a reduction or an enlargement? explain your reasoning.

can someone also give me the rest of the answers for rising, running, stepping, scaling part 2 quiz

Because the scale factor is at the origin, you multiply all the coordinates by the scale factor:

Q(-3,7) = Q'(-3*3, 7*3) = Q'(-9,21)

R(-3,11) = R(-3*3, 11*3) = R'(-9,33)

S(4,11) = S'(4*3,11*3) = R'(12,33)

T(4,7) = T'(4*3, 7*3) = T'(12,21)

Q'(-9,21), R'(-9,33), S'(12,33) and T'(12,21)

It is enlargement.

Step-by-step explanation:

Given : Rectangle QRST has coordinates Q (− 3 , 7 ) , R (− 3 , 11 ) , S ( 4 , 11 ) , and T ( 4 , 7 ) .

Scale factor =3 >1 , so it is an enlargement.  [Figure enlarge using scale factor greater than 1 ]

The rule we use for dilating a figure using center of dilation at the origin and scale factor k:

Then, the coordinates of rectangle Q 'R 'S 'T ' will be :-

Hence, the coordinates of rectangle Q 'R 'S 'T ' are : Q'(-9,21), R'(-9,33), S'(12,33) and T'(12,21)

its an acute right triangle

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240