×
Geometry

# 2D Coordinate Geometry - Problem Solving

I left my house and walked 800 meters north, before I reached the traffic intersection.
I then turned right, and walked a further 1500 meters east, to reach the amusement park.

What is the straight-line distance (in meters) from my house to the amusement park?

$$a, b, c$$ are real constants such that all the lines represented by $$ax+by+c=0$$ are concurrent at a point $$P$$. This point $$P$$ lies on the line $$ax+by+c=0$$ such that $$7a+2b+8c=0$$. What are the coordinates of $$P$$?

Find the equation of the line which is tangent to the circle $(x-3)^2 + (y-11)^2 = 53$ at the point $$P = ( 5, 4).$$

If four points on the $$xy$$-plane $$A=(-1, a)$$, $$B=(b, 0)$$, $$C=(15, 1)$$, and $$D=(2, 21)$$ are the vertices of parallelogram $$ABCD$$, what is the value of $$a + b$$?

Parallelogram $$ABCD$$ has three vertices $A=(28, 24),\ B=(3,4) \textrm{ and }\ C=(14, 36).$ If the intersection point of the two diagonals $$AC$$ and $$BD$$ is $$M=(a,\ b)$$, what is the value of $$a + b$$?

×

Problem Loading...

Note Loading...

Set Loading...