Coordinate Geom...

In the standard $$(x,y)$$ coordinate plane, what are the coordinates of the midpoint of a line segment whose endpoints are $$(-3,0)$$ amd $$(7,4)$$?

In figure, if the midpoints of segments $$\overline{GH}, \overline{JK}$$, and $$\overline{LM}$$ are connected, calculate the area of the resulting triangle.

Calculate the area of a triangle with vertices $$(1, 1), (3, 1)$$ and $$(5, 7)$$.

Points $$A(\sqrt {2}, 4), B(6, -\sqrt {3})$$ and $$C$$ are collinear. If $$B$$ is the midpoint of line segment $$AC$$, approximately calculate the $$(x, y)$$ coordinates of point $$C$$.

Given point $$A(-3, -8)$$, if the midpoint of segment $$AB$$ is $$(1, -5)$$, calculate the coordinates of point $$B$$.

The area of the triangle with coordinates $$(1, 2), (5, 5)$$ and $$(k, 2)$$ is $$15$$ square units. Calculate a possible value for $$k$$.

Find the area of a triangle whose vertices are $$(0, 6\sqrt {3}), (\sqrt {35}, 7)$$, and $$(0, 3)$$.

A square is formed by the points $$(4, 5), (12, 5), (12, -3)$$ and $$(4, -3)$$. Find the coordinates of the point at which the diagonals of the square intersect.

If the coordinates of the one end of a diameter of a circle are $$(2,3)$$ and the coordinates of its centre are $$(-2,5),$$ then the coordinates of the other end of the diameter are:

In fig., the area of triangle ABC (in sq. units) is: