A triangle in the plane has vertices at A(-2,-4), B(-1,5) and C(4, -3). This triangle is shifted horizontally left 2 units and then vertically up 3 units, find the coordinates of the new vertices.
The vertices of a second triangle are symmetric to the vertices of the above triangle with respect to the origin. What are the coordinates of the vertices of this second triangle?

Question

A triangle in the plane has vertices at A(-2,-4), B(-1,5) and C(4, -3). This triangle is shifted horizontally left 2 units and then vertically up 3 units, find the coordinates of the new vertices. 
        The vertices of a second triangle are symmetric to the vertices of the above triangle with respect to the origin. What are the coordinates of the vertices of this second triangle?

anonymous · Answer

For the second part, the question is referring to central symmetry about the origin. What that means is you take the point you're looking at (say A(-2,-4)) as an example in this case), draw a line from there through the origin, and mark another point on that line (let's call it A')that is the same distance from O as A is. So the distance |OA| = |OA'|.

You can break down those distances into horizontal and vertical components. If A is at (-2,-4), then you can tell that it is '2' away from the origin along the x-axis, and '4' away from the origin on the y-axis. The point A' will also be '2' away from the origin along the x-axis (but in the other direction to A|dw:1315245563540:dw|), and '4' away from the origin along the y-axis (again, in the other direction to A)