Well this is my thought depending on where the point of dilation is the coordinates of the give plane is determined. The point of dilation not only is main factor that positions the coordinates, but the scale factor has a huge impact on the placement of the coordinates.
The coordinates of all points in the coordinate plane consist of ordered pairs of numbers.
Two coordinates define a point. You need two pairs of two coordinates to define two points and, therefore, a slope.
No.
It is simply the difference between their y coordinates.
You need two coordinates, not one, to specify a point. To calculate the slope, simply calculate (difference in y-coordinates) / (difference in x-coordinates).
To solve a dilation problem, you first need to identify the center of dilation and the scale factor. The scale factor indicates how much larger or smaller the figure will be compared to the original. For each point on the original figure, you calculate the new coordinates by multiplying the distances from the center of dilation by the scale factor. Finally, plot the new points to create the dilated figure.
Invariant points of a dilation are the points that remain unchanged under the transformation. In a dilation centered at a point ( C ) with a scale factor ( k ), the invariant point is typically the center ( C ) itself. This means that when a point is dilated with respect to ( C ), it either moves closer to or further away from ( C ), but ( C ) does not move. Therefore, the only invariant point in a dilation is the center of dilation.
To find the image of points A, B, and C after a dilation centered at the origin with a scale factor of 2, you multiply each coordinate by 2. The new coordinates are A'(12, 14), B'(8, 4), and C'(0, 14). Thus, the images of the points after dilation are A'(12, 14), B'(8, 4), and C'(0, 14).
To dilate the points S, P, O, and T by a scale factor of 3 centered at the origin, you multiply the coordinates of each point by 3. If the original coordinates of S, P, O, and T are (x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄) respectively, the new coordinates after dilation will be (3x₁, 3y₁), (3x₂, 3y₂), (3x₃, 3y₃), and (3x₄, 3y₄).
To graph a dilation, first identify the center of dilation and the scale factor. For each point of the original figure, measure the distance from that point to the center of dilation, then multiply that distance by the scale factor to find the new distance from the center. Plot the new points at these distances, and connect them to form the dilated figure. Ensure that the orientation remains the same and that the shape is proportional to the original.
-- The 'x' coordinate of the midpoint is the average of the 'x'-coordinates of the end-points. -- The 'y' coordinate of the midpoint is the average of the 'y'-coordinates of the end-points.
The coordinates of all points in the coordinate plane consist of ordered pairs of numbers.
The equation does not have and y variable in it: it is of the form x = c. Alternatively, the x coordinates of both points are the same and the y coordinates are not.
To determine the coordinates of point D in trapezium ABCD, we need the coordinates of points A, B, and C, as well as the requirement that one pair of opposite sides (either AB and CD or AD and BC) are parallel. If AB is parallel to CD, then the y-coordinates of points A and B must equal the y-coordinates of points C and D, respectively. Alternatively, if AD is parallel to BC, then the x-coordinates of A and D must equal the x-coordinates of B and C. Please provide the specific coordinates of points A, B, and C for a precise answer.
Properties such as parallelism, ratio of distances, and the measure of angles are preserved under dilation. This means that parallel lines remain parallel after dilation, the ratio of lengths between corresponding points remains constant, and angles maintain their measures before and after dilation.
Intersection or coordinates
By giving their coordinates.