A figure has a 30° angle located at the point (−6,−8) . What is the coordinate point for this angle when the figure is translated (x+4, y−1) ?
(6,8)
(−2,−9)
(−10,−7)
(6,−8)
To translate the point (-6,-8) by (x+4, y-1), we add 4 to the x-coordinate and subtract 1 from the y-coordinate:
x + 4 = -6 + 4 = -2
y - 1 = -8 - 1 = -9
Therefore, the new coordinates of the figure after translation are (-2,-9), which corresponds to the option (−2,−9).
A polygon has an angle that measures 77°. When the polygon is rotated 90°, what will be the measurement of the angle?
167°
77°
103°
90°
When a polygon is rotated by 90°, all of its angles are also rotated by 90°. Therefore, if an angle in the original polygon measures 77°, when the polygon is rotated by 90°, the new measurement of the angle will be 77° + 90° = 167°.
So, the correct answer is 167°.
Which statement accurately describes what happens to parallel lines during a reflection?
They remain parallel.
They intersect at an obtuse angle.
They intersect at an acute angle.
They become perpendicular.
The correct statement is: They remain parallel.
Darius draws a regular hexagon on the coordinate plane. He then translates the hexagon up 3 units and to the left 2 units. How many sets of parallel sides will the translated hexagon have?
2
0
1
3
The translated hexagon will have 0 sets of parallel sides.
Translation does not change the shape or orientation of a polygon, it only moves it in a certain direction. Since the original hexagon is a regular hexagon, it has 3 sets of parallel sides. However, after translating it up 3 units and to the left 2 units, the hexagon is displaced in such a way that none of its sides remain parallel to each other. Therefore, the translated hexagon will have 0 sets of parallel sides.
A square is rotated 45° on the coordinate plane. Which statement is true?
Both the original square and the rotated square have exactly two pairs of parallel sides.
The original square has two pairs of parallel sides, but the rotated square has no pairs of parallel sides.
Both the original square and the rotated square have exactly one pair of parallel sides.
The original square has no pairs of parallel sides, but the rotated square has two pairs of parallel sides.
The correct statement is: Both the original square and the rotated square have exactly two pairs of parallel sides.
A square has four equal sides and four right angles. In the original square, opposite sides are parallel, making two pairs of parallel sides. When a square is rotated 45° on the coordinate plane, it still retains its shape and properties. The rotated square will also have two pairs of parallel sides, just like the original square.