Straight Lines ...

In the diagram $$MN$$ is a straight line on a Cartesian plane. The coordinates of $$N$$ are $$(12,13)$$ and $${MN}^{2}=9$$ units. The coordinates of $$M$$ are:

In the figure, $$AC = 9, BC = 3$$ and $$D$$ is $$3$$ times as far from $$A$$ as from $$B$$. What is $$BD$$?

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?

If the area of the triangle shown is $$30$$ square units, what is the value of $$y$$?

If the distance between the two points $$P(a,3)$$ and $$Q(4,6)$$ is $$5$$, then find $$a$$.

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.

If figure $$\Box ABCD$$ABCD is a parallelogram, what is the x-coordinate of point B?

In the diagram, $$PQR$$, is an isosceles triangle and $$QR=5$$ units.
The coordinates of $$Q$$ are:

In the figure, there is a regular hexagon with sides of length $$6$$. If the coordinate of $$A$$ is $$(9,0)$$, what is the y-coordinate of $$B$$?

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?