Coordinate Geometry

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Coordinate Geometry & Line Formula

Distance Formula \(\left | P_{1}P_{2} \right |=\sqrt{\left ( x_{2}-x_{1} \right )^{2}+\left ( y_{2}-y_{1} \right )^{2}}\)
Slope \(\large m=\frac{rise}{run}=\frac{\Delta y}{\Delta x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Point-Slope Form \(y-y_{1}=m\left ( x-x_{1} \right )\)
Point-Point Form \(y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left ( x-x_{1} \right )\)
Slope-Intercept Form \(y=mx+b\)
Intercept-Intercept Form \(\frac{x}{a}+\frac{y}{b}=1\)
General Form \(Ax+By+C=0\)
Parallel & Perpendicular Lines Parallel Lines \(m_{1}=m_{2}\)
Perpendicular Lines \( m_{1}m_{2}=-1\)
Distance from a Point to a Line \(\large d=\frac{\left | Ax_{0}+By_{0}+C \right |}{\sqrt{A^{2}+B^{2}}}\)

1 Point P is the midpoint of segment AB. Co-ordinates of point P are (2,1) and point A are (11,5). Co-ordinates of point B are

A
(-7,-3)
B
(6.5,3)
C
(7,3)
D
(-6.5,-3)

2 The angle made by the line x + √3y - 6 = 0, with positive direction of x-axis is:

A
120°
B
150°
C
30°
D
60°

3 The line passing through point (-3,1) and point (x,5) is parallel to the line passing through point (-2,-1) and point (6,3). What is the value of x?

A
-5
B
-2
C
2
D
5

4 Find the slope of the line whose equation is 4y +12x - 1 = 0

A
-3
B
3
C
2
D
12

5 In which of the following lines, do these two point (1,3) and (2,6) lies?

A
y = x+ 2
B
y = x + 4
C
y = 3x
D
y=2x

6 Equation of line passing through (1, 4) and perpendicular to y = 2x + 3 is? 

A
2y = x + 7
B
y = 2x + 2
C
2y +×= 9
D
y + 2x = 6

7 Find the distance between the points (2,2) and (-1,6) 

A
5 unit's
B
4 unit's
C
7 unit's
D
√(26) unit's

8 The shortest distance of the point (4,8) form the X-Axis is 

A
12
B
6
C
sqrt(80)
D
8

9 Find the area of the triangle whose coordinates are (1, 2) , (3, 4) and (5, 10)

A
3
B
4
C
5
D
8

10 Find the center of the circle whose end points of the diameters are (2,10) and (6,2). 

A
(4,12)
B
(2,6)
C
(4,8)
D
(4,6)