2D Coordinate 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,ca, b, c are real constants such that all the lines represented by ax+by+c=0ax+by+c=0 are concurrent at a point PP. This point PP lies on the line ax+by+c=0ax+by+c=0 such that 7a+2b+8c=07a+2b+8c=0. What are the coordinates of PP?

Find the equation of the line which is tangent to the circle (x3)2+(y11)2=53 (x-3)^2 + (y-11)^2 = 53 at the point P=(5,4).P = ( 5, 4).

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

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


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