Coordinate Geom...

The vertices of a triangle ABC are $$(\lambda, 2 - \lambda), (- \lambda + 1, 2 \lambda) $$ and $$(-4 - \lambda, 6 - 2 \lambda)$$. If its area is 70 units$$^2$$, find the number of integral values of $$\lambda$$.

In the diagram, $$KN$$ is a straight line. $$L$$ and $$M$$ are two points on $$KN$$ such that $$KL=LM$$ and $$KM=MN$$. Find the coordinates of $$L$$.

$$A(-3,2)$$ and $$B(5,4)$$ are the end points of a line segment, find the coordinates of the midpoints of the line segment.

The area of a triangle is 5 and its two vertices are A(2, 1) and B(3, -2). The third vertex lies on $$\displaystyle y=x+3$$. What is the third vertex?

In the $$xy$$-plane, the vertices of a triangle are $$(-1,3), (6,3)$$ and $$(-1,-4)$$. The area of the triangle is ___ square units.

The vertices of triangle $$PQR$$ are $$P(-3, 2), Q(1, -4)$$, and $$R(7, 0)$$. The altitude drawn from Q intersects the line $$PR$$ at the point

Two vertices of a triangle are (2, 1) and (3, -2). Its third vertex is (x, y) such that $$\displaystyle y=x+3$$. If its area is 5 sq. units, what are the co-ordinates of the third vertex?

Area of the triangle formed by the points $$\left( 0,0 \right) ,\left( 2,0 \right) $$ and $$\left( 0,2 \right) $$ is 

Find the midpoint of the line segment joining the points $$(1,-1)$$ and $$(-5,-3)$$.

The centre of a circle is at $$(-6,4)$$. If one end of a diameter of the circle is at the origin, then find the other end.