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2. Points are Collinear or Triangle or Quadrilateral form example
( Enter your problem )
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- Determine if the points A(1,5), B(2,3), C(-2,-11) are collinear points
- Show that the points A(-3,0), B(1,-3), C(4,1) are vertices of a right angle triangle
- Show that the points A(1,1), B(-1,-1), C(-1.732051,1.732051) are vertices of an equilateral triangle
- Show that the points A(7,10), B(-2,5), C(3,-4) are vertices of an isosceles triangle
- Determine if the points A(0,0), B(2,0), C(-4,0), D(-2,0) are collinear points
- Show that the points A(1,2), B(5,4), C(3,8), D(-1,6) are vertices of a square
- Show that the points A(-4,-1), B(-2,-4), C(4,0), D(2,3) are vertices of a rectangle
- Show that the points A(3,0), B(4,5), C(-1,4), D(-2,-1) are vertices of a rhombus
- Show that the points A(-3,-2), B(5,-2), C(9,3), D(1,3) are vertices of a parallelogram
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Other related methods
- Distance, Slope of two points
- Points are Collinear or Triangle or Quadrilateral form
- Find Ratio of line joining AB and is divided by P
- Find Midpoint or Trisection points or equidistant points on X-Y axis
- Find Centroid, Circumcenter, Area of a triangle
- Find the equation of a line using slope, point, X-intercept, Y-intercept
- Find Slope, X-intercept, Y-intercept of a line
- Find the equation of a line passing through point of intersection of two lines and slope or a point
- Find the equation of a line passing through a point and parallel or perpendicular to Line-2 or point-2 and point-3
- Find the equation of a line passing through point of intersection of Line-1, Line-2 and parallel or perpendicular to Line-3
- For two lines, find Angle, intersection point and determine if parallel or perpendicular lines
- Reflection of points about x-axis, y-axis, origin
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4. Show that the points A(7,10), B(-2,5), C(3,-4) are vertices of an isosceles triangle
(Previous example) | 6. Show that the points A(1,2), B(5,4), C(3,8), D(-1,6) are vertices of a square
(Next example) |
5. Determine if the points A(0,0), B(2,0), C(-4,0), D(-2,0) are collinear points
1. Determine if the points `A(0,0), B(2,0), C(-4,0), D(-2,0)` are collinear points
Solution:
We know that the distance between the two points `(x_1,y_1)` and `(x_2,y_2)` is
`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
The given points are `A(0,0),B(2,0),C(-4,0),D(-2,0)`
`CD=sqrt((-2+4)^2+(0-0)^2)`
`=sqrt((2)^2+(0)^2)`
`=sqrt(4+0)`
`=sqrt(4)`
`:. CD=2`
`DA=sqrt((0+2)^2+(0-0)^2)`
`=sqrt((2)^2+(0)^2)`
`=sqrt(4+0)`
`=sqrt(4)`
`:. DA=2`
`AB=sqrt((2-0)^2+(0-0)^2)`
`=sqrt((2)^2+(0)^2)`
`=sqrt(4+0)`
`=sqrt(4)`
`:. AB=2`
`CB=sqrt((2+4)^2+(0-0)^2)`
`=sqrt((6)^2+(0)^2)`
`=sqrt(36+0)`
`=sqrt(36)`
`:. CB=6`
Here `CD+DA+AB=2+2+2=6=CB`
`:.` C,D,A,B are collinear points
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
4. Show that the points A(7,10), B(-2,5), C(3,-4) are vertices of an isosceles triangle
(Previous example) | 6. Show that the points A(1,2), B(5,4), C(3,8), D(-1,6) are vertices of a square
(Next example) |
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