The transformation described is known as a translation. In a translation, each point of a shape or object is moved a specified distance in a direction parallel to a given line. This results in the entire shape retaining its orientation and size while being repositioned in the coordinate plane.
Parallel
A transformation that shifts all the points in a plane figure without altering the shape of the figure is called a "translation." During a translation, each point of the figure moves the same distance in a specified direction, resulting in a congruent figure in a new position. This operation maintains the figure's size, shape, and orientation.
Parallel lines will never intersect. They will stay an equal distance apart at all points.
Lines can by parallel or not parallel. This property does not apply to points.
Rotation transformations move all points in a plane around a fixed point, known as the center of rotation, by a specified angle. Every point is rotated to a new position, maintaining the same distance from the center, resulting in a consistent change in the orientation of the shape or object. This transformation preserves the shape and size while altering its position.
Reflection
Suppose the specified line has gradient m. Also suppose the specified distance is d.Then x = sqrt[d2/(1 + m2)] and y = m*x.A translation, by a distance x in the horizontal direction and y=mx in the vertical direction will move the point by the specified distance in the direction of the specified line.
A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).
translation
Two or more lines that are the same distance at all points are called parallel lines.
the same distance
Parallel
Yes, in geography, all points along a parallel of latitude are indeed the same distance from the equator. This is because parallels are imaginary lines that run parallel to the equator, maintaining the same distance from it as they wrap around the Earth.
The locus of points at a given distance to a line would be a line parallel to the first line. Assuming that both lines are straight.
Parallel lines are the same distance apart for all points along the line.
A transformation that shifts all the points in a plane figure without altering the shape of the figure is called a "translation." During a translation, each point of the figure moves the same distance in a specified direction, resulting in a congruent figure in a new position. This operation maintains the figure's size, shape, and orientation.
Parallel lines will never intersect. They will stay an equal distance apart at all points.