The measure of an angle is 51 degrees
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A reflection about a line gives an image that is at an equal distance from the line but on the opposite (other) side of the line
The distance between the lines <em>m</em> and <em>n</em> is <u>6 units</u>
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Reason:
The given parameters are;
Let <em>Y</em> represent the top vertex of Δ(XYZ), and the coordinates of point <em>Y</em> is (3, 0) we have;
The coordinates of Y following is Y''(3, -12)
A reflection of <em>Y </em> across the line m, y = -9, gives the coordinates of the image at Y'(3, -18)
A reflection of the image Y'(3, -18) across the line n, y = -15, gives the image at Y''(3, -12)
The distance between lines <em>m</em>, and line <em>n</em>, is -9 - (-15) = 6
Generally, the difference between two lines of reflection, <em>n</em>, and <em>m</em>, following a composite reflection is 2×(n - m)
Given that the total transformation is -12, we have;
2×(n - m) = -12
Therefore;
Which gives;
m - n = 6
The distance between the two lines = 6 units
Learn more about reflection about a line here;
The dimensions of the rectangle can be a length of 2ft and a width of 4ft.
<h3>How to find the dimensions of the garden?</h3>
Remember that for a rectangle of length L and width W, the perimeter is:
P = 2*(L + W)
And the area is:
A = L*W
In this case, we know that the area is 8 square feet and the perimeter is 12 ft, then we have a system of equations:
12ft = 2*(L + W)
8ft² = L*W
To solve this, we first need to isolate one of the variables in one of the equations, I will isolate L on the first one:
12ft/2 = L + W
6ft - W = L
Now we can replace that in the other equation to get:
8ft² = (6ft - W)*W
This is a quadratic equation:
-W^2 + 6ft*W - 8ft² = 0
The solutions are given by Bhaskara's formula:
Then we have two solutions:
W = (-6 - 2)/-2 = 4ft
W = (-6 + 2)/-2 = 2ft
If we take any of these solutions, the length will be equal to the other solution.
So the dimensions of the rectangle can be a length of 2ft and a width of 4ft.
if you want to learn more about rectangles:
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