The centre of the rotation is A
The line of the reflection is Y
Vertex A of the triangle ABC when rotated by 90° counterclockwise about the origin,
Rule to be followed,
A(x, y) → P(-y, x)
Therefore, A(1, 1) → P(-1, 1)
Similarly, B(3, 2) → Q(-2, 3)
C(2, 5) → R(-5, 2)
Triangle given in second quadrant will be the triangle PQR.
If the point P of triangle PQR is reflected across a line y = x,
Rule to be followed,
P(x, y) → X(y, x)
P(-1, 1) → X(1, -1)
Similarly, Q(-2, 3) → Y(3, -2)
R(-5, 2) → Z(2, -5)
Therefore, triangle given in the fourth quadrant is triangle XYZ.
Learn more about reflection
brainly.com/question/13805069
#SPJ9
Simplifying
5C + -4 + -2C + 1 = 8C + 2
Reorder the terms:
-4 + 1 + 5C + -2C = 8C + 2
Combine like terms: -4 + 1 = -3
-3 + 5C + -2C = 8C + 2
Combine like terms: 5C + -2C = 3C
-3 + 3C = 8C + 2
Reorder the terms:
-3 + 3C = 2 + 8C
Solving
-3 + 3C = 2 + 8C
Solving for variable 'C'.
Move all terms containing C to the left, all other terms to the right.
Add '-8C' to each side of the equation.
-3 + 3C + -8C = 2 + 8C + -8C Combine like terms: 3C + -8C = -5C<span>-3 + -5C = 2 + 8C + -8C
Combine like terms: 8C + -8C = 0
-3 + -5C = 2 + 0
-3 + -5C = 2
Add '3' to each side of the equation.
-3 + 3 + -5C = 2 + 3
Combine like terms: -3 + 3 = 0
0 + -5C = 2 + 3
-5C = 2 + 3
Combine like terms: 2 + 3 = 5
-5C = 5
Divide each side by '-5'.
C = -1
Simplifying
C = -1</span>
Answer:
"The area of EFGH is always One-half of the area of the rectangle."
Step-by-step explanation:
<em>Graph is attached.</em>
<em />
The kite consists of 2 triangle, EFG and EHG.
The area of EFG:

where h is the height from F to EG
The area of EHG:

where
is the height from H to EG
We also know that h + h _1 is the width of the rectangle and EG is the length of the rectangle
Thus,
Area of Kite = 
Also, Area of rectangle is rectangle length * rectangle width.
Thus, area of kite is always half of that of rectangle, the third choice is right.