The kite shown below is translated 8 units to the right and 1 unit up.
Which property will remain the same?
A.
the coordinates of the x-intercept
B.
the perimeter of the kite
C.
the angle between the top vertex and the origin
D.
the coordinates of the vertices
D. the coordinates of the vertices
D. the coordinates of the vertices
To determine which property remains the same after the translation, let's consider each option.
A. The coordinates of the x-intercept: The x-intercept is the point where the graph of the kite intersects the x-axis. Since the kite has been translated 8 units to the right, the x-coordinate of the x-intercept will change. Therefore, option A is not correct.
B. The perimeter of the kite: The perimeter of a shape is defined as the sum of the lengths of its sides. In this case, the kite has been translated by shifting each point 8 units to the right and 1 unit up. This translation does not affect the lengths of the sides of the kite. Therefore, the perimeter of the kite remains the same. Thus, option B is correct.
C. The angle between the top vertex and the origin: The angle between the top vertex of the kite and the origin (0,0) will change after the translation. The shift will affect the position of the top vertex relative to the origin, so the angle will not remain the same. Therefore, option C is not correct.
D. The coordinates of the vertices: The translation specifies that the kite is shifted 8 units to the right and 1 unit up. This means that all the points of the kite will experience the same translation. Consequently, the coordinates of each vertex will change according to the translation but maintain the same relative positions. Therefore, option D is not correct.
In conclusion, the correct answer is B. The perimeter of the kite will remain the same after the translation, while the other properties will change.