Original vertices:
1 (-3, 2)
2 (-5,-4)
3 ( 4, 6)
4 ( 7, 0)
dilated by a scale factor of 0.50
1) -3*0.50 = -1.5 ; 2 * 0.50 = 1 ⇒ (-1.5,1)
2) -5*0.50 = -2.5 ; -4*0.50 = -2 ⇒(-2.5,-2)
3) 4*0.50 = 2; 6*0.50 = 3 ⇒ (2,3)
4) 7*0.50 = 3.5; 0*0.50 = 0 ⇒ (3.5,0)
B.)
-1.5 -2.5 2 3.5
<span> 1 -2 3 0 </span>
Let the length of the playground be x, then the width is 6 + x.
Area = length * width = x * (6 + x) = 6x + x^2 = 216
Solving the quadratic equation x^2 + 6x - 216 = 0, we have x = 12 or -18
i.e length = 12 and width = 6 + 18 = 18
Answer:
The other side was decreased to approximately .89 times its original size, meaning it was reduced by approximately 11%
Step-by-step explanation:
We can start with the basic equation for the area of a rectangle:
l × w = a
And now express the changes described above as an equation, using "p" as the amount that the width is changed:
(l × 1.1) × (w × p) = a × .98
Now let's rearrange both of those equations to solve for a / l. Starting with the first and easiest:
w = a/l
now the second one:
1.1l × wp = 0.98a
wp = 0.98a / 1.1l
1.1 wp / 0.98 = a/l
Now with both of those equalling a/l, we can equate them:
1.1 wp / 0.98 = w
We can then divide both sides by w, eliminating it
1.1wp / 0.98w = w/w
1.1p / 0.98 = 1
And solve for p
1.1p = 0.98
p = 0.98 / 1.1
p ≈ 0.89
So the width is scaled by approximately 89%
We can double check that too. Let's multiply that by the scaled length and see if we get the two percent decrease:
.89 × 1.1 = 0.979
That should be 0.98, and we're close enough. That difference of 1/1000 is due to rounding the 0.98 / 1.1 to .89. The actual result of that fraction is 0.89090909... if we multiply that by 1.1, we get exactly .98.
M = (1,4)
N = (5,2)
For M, you simply move to 1 on the x axis abs for 4 you move on the y axis. Same does for N, for 5 you move on the x axis and for 2 you move on the y axis.
200in^2
The face is made up of 2 squares which have side lengths of 10, 10 times 10 equals 100 and there’s 2 of them which makes 100+100=200in^2
