Coordinate Geometry Questions
Distance Formula: d = (x2 - x1)2 + (y2 - y1)2

1. Find the distance between the points
(a) (0, 2) and (3, 6) (b) (-2, 3) and (4, -5) (c) (2, -5) and (-3, 7)
2. Find the exact length of the interval between points
(a) (2, 3) and (-1, 1) (b) (-1, 3) and (-7, 7)
3. Prove that the triangle with vertices (3, 4), (-2, 7) and (6, -1) is isosceles.
4. Show that the points (3, -4) and (8, 1) are equidistant from the point (7, -3).
5. Prove ....etc

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In-Home Coordinate System: Currently, many household, self-automated robots (lawn mowers or vacuum cleaners) covers area with a random algorithm, often using 5 hours to do something it should be done in 2 since it goes over the same spot may times. Usually, it uses an infrared or other sensor system to detect obstacles and boundaries. However, the path of the robot could be more controlled if there was a way to set up a ”coordinate system” for the robot to follow. This would allow the user to only clean/mow specific areas, or in a ....etc

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ENHANCEMENT OF VEHICLE STABILITY BY ACTIVE GEOMETRY
CONTROL SUSPENSION SYSTEM
1. INTRODUCTION
In recent years, there has been increased need to develop high-performance suspension for high-power engines ,especially active chassis control systems have been developed and mass-produced in the market to compromise vehicle ride and handling performance simultaneously,
The conventional active chassis control systems control the vehicle phenomenon such as body roll, yaw, and pitch using hydraulic actuators w ....etc

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