Problems in Plane Analytic Geometry: Problems with Solutions

Problem 1
Find the distance between A(5, -3) and B(2, 1).
Problem 2
Find the slope of a line, which passes through point А(5, -3) and meets y axis at 7.
Problem 3
The equation of the line through points $P_{1}(1,3)$ and $P_{2}(-2,1)$ is
Problem 4
A line with equation $y=mx+b$ passes through the points $P_{1}(-2,2)$ and $P_{2}(2,0)$. What are the values of $m$ and $b$?
Problem 5
Find the equation of a line which passes through A(4, -1) and is parallel to x axis.
Problem 6
Find the equation of a line which intercept y axis at -4 and also intercept x axis at 2.
Problem 7
Find the distance between A(2, -3) and the line L:3x - 4y + 2 = 0.
Problem 8
Find the area of a triangle with vertices: A(0, -3), B(5, 0), C(0, 3).
Problem 9
What is the area of triangle with vertices $P(1,1),Q(-1,2),R(2,-1)$
Problem 10
If the distance of A(2x - 3, 5) from line x = -4 is equal to 7, then find the value of a.
Answer format: m,n where m < n

Problem 11
Find the value of m, such that D1, D2, D3 meet each other at one point.
D1: x - y = 1
D2: 2x + y = 5
D3: (2m - 5)x - my = 3
Answer format: p/q
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