What is the image of (9, 3) after a dilation by a scale factor of 3 centered at the origin?
2 answers:
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Answer:
HK = 20
Step-by-step explanation:
LM = (1/2) HK {Mid point theorem}
2*(10x - 90) = 10x - 80
2*10x - 2*90 = 10x - 80
20x - 180 = 10x - 80 {add 180 to both sides}
20x = 10x - 80 + 180
20x = 10x +100 {Subtract 10x from both sides from }
20x -10x = 100
10x = 100
x = 100/10
x = 10
HK = 10x - 80
= 10*10 - 80
= 100 - 80
= 20
The question is incomplete. Here is the complete question.
Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.
Answer: L = 1; W = 9/4; A = 2.25;
Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:
A = x.y
A = x(-)
A = -
To maximize, we have to differentiate the equation:
=
(-
)
= -3x + 3
The critical point is:
= 0
-3x + 3 = 0
x = 1
Substituing:
y = -x + 3
y = -.1 + 3
y = 9/4
So, the measurements are x = L = 1 and y = W = 9/4
The maximum area is:
A = 1 . 9/4
A = 9/4
A = 2.25
