How many solutions does the system have?
2 answers:
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Answer:
The ∠B prime A prime C prime in the resulting figure = 90°
Step-by-step explanation:
The coordinates of the right triangle = A( -1, 4), B(-1, 8) and C(3, 4)
The rotation 90° counterclockwise of a point on a preimage (x, y) gives the coordinates of the location of the point of the image after rotation as (-y, x)
Therefore we have;
Applying 90° counterclockwise rotation we have;
- The point A(-1, 4) is relocated to the point (-4, -1)
- The point B(-1, 8) is relocated to the point (-8, -1)
- The point C(3, 4) is relocated to the point (-4, 3)
Applying a translation T(-2, -3) to the new points above which is a translation 2 units left and 3 units down, we have;
The coordinates of the point A prime is (-4 - 2, -1 - 3) = (-6, -4)
The coordinates of the point B prime is (-8 - 2, -1 - 3) = (-10, -4)
The coordinates of the point C prime is (-4 - 2, 3 - 3) = (-6, 0)
The coordinates of the vertices of the triangle ΔA prime B prime C prime are A prime (-6, -4) B prime (-10, -4) C prime (-6, 0)
The measure of the angle ∠B prime A prime C prime is given as follows;
Length of a segment of each segment of the triangle are found using the following equation;
Which gives;
Length of B prime A prime = √(((-10) - (-6))² + ((-4) - (-4))²) = 4
Length of B prime C prime = √(((-10) - (-6))² + ((-4) - 0)²) = 32 = 4·√2
Length of C prime A prime = √(((-6) - (-6))² + ((0) - (-4))²) = 4
∴ B prime C prime is the hypotenuse side and the ∠B prime A prime C prime = The angle opposite to the hypotenuse side = 90°
The ∠B prime A prime C prime in the resulting figure = 90°