Answer:
The coordinates of vertex A' are (3, 5).
Explanation:
Before we do anything, first we must understand what a dilation is. A dilation is the scaling of a shape by a ratio that scales its side lengths but overall maintains the same shape and angles, with a point of dilation that the shape dilates from.
In this scenario, we are given a shape, a point of dilation, and a dilation ratio. The problem asks for us to find the coordinate of a vertex of the shape after it has dilated, so we can focus on just the single point instead of the whole shape. On the coordinate plane, the point of dilation - X - has a coordinate of (1, 9). On the other hand, point A has a coordinate of (2, 7). This means point A is 2 units down and 1 unit to the right of point X. Since the trapezium is being dilated by a scale factor by 2, that means every change in x and y-values will be multiplied by 2 to create the new point A'. So point A' would be 4 units down and 2 units to the right of point X, and have the coordinates (1 + 2, 9 - 4) or (3, 5). Therefore, the coordinates of vertex A' are (3, 5).
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