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1 answer:
9514 1404 393
Answer:
a) M(2,2), B(4, -2), D(0, 6)
b) 40
Step-by-step explanation:
a) The midpoint of AC is the average of the endpoint coordinates.
M = (A +C)/2
M = ((-2, 0) +(6, 4))/2 = (4, 4)/2
M = (2, 2)
There are several ways to find points B and D. One of them is to rotate points A and C 90° about M. The 90° CCW rotation transformation about the origin is ...
(x, y) ⇒ (-y, x)
About the point (2, 2), the transformation would be ...
(x, y) ⇒ (-(y -2)+2, (x -2)+2) = (4 -y, x)
Rotating point A 90° to get point B, we have ...
B = (4 -0, -2)
B = (4, -2)
And rotating C to get point D, we have ...
D = (4 -4, 6)
D = (0, 6)
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b) The area of the square is half the square of the diagonal. The square of the diagonal can be found using the distance formula ...
d² = AC² = (6-(-2))² +(4 -0)² = 64 +16 = 80
Then the area is ...
area = AC²/2 = 80/2
area = 40 . . . . square units
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Answer:
m = 3, n = 6
Step-by-step explanation:
The hypotenuse leg (HL) theorem states that two triangles are said to be similar if one leg and the hypotenuse of the triangles are congruent.
From the diagram, comparing the hypotenuse of the triangles;
4m + 1 = 13
4m = 13 - 1
= 12
m =
= 3
m = 3
Also, comparing the sides;
2m + n = 8m - 2n
substitute the value of m to have,
6 + n = 24 - 2n
collect like terms,
n + 2n = 24 - 6
3n = 18
n =
= 6
n = 6
m = 3, n = 6