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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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2. Show that the points A(-3,0), B(1,-3), C(4,1) are vertices of a right angle triangle
(Previous example) | 4. Show that the points A(7,10), B(-2,5), C(3,-4) are vertices of an isosceles triangle
(Next example) |
3. Show that the points A(1,1), B(-1,-1), C(-1.732051,1.732051) are vertices of an equilateral triangle
1. Show that the points `A(1,1), B(-1,-1), C(-1.732051,1.732051)` are vertices of an equilateral triangle
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)`
A Triangle, in which all sides are equal, is called an equilateral triangle
The given points are `A(1,1),B(-1,-1),C(-1.7321,1.7321)`
`AB=sqrt((-1-1)^2+(-1-1)^2)`
`=sqrt((-2)^2+(-2)^2)`
`=sqrt(4+4)`
`=sqrt(8)`
`:. AB=2sqrt(2)`
`BC=sqrt((-1.7321+1)^2+(1.7321+1)^2)`
`=sqrt((-0.7321)^2+(2.7321)^2)`
`=sqrt(0.5359+7.4641)`
`=sqrt(8)`
`:. BC=2sqrt(2)`
`AC=sqrt((-1.7321-1)^2+(1.7321-1)^2)`
`=sqrt((-2.7321)^2+(0.7321)^2)`
`=sqrt(7.4641+0.5359)`
`=sqrt(8)`
`:. AC=2sqrt(2)`
Here `AB=BC=AC`
`:.` ABC is an equilateral triangle
2. Show that the points `A(2,5), B(8,5), C(5,10.196152)` are vertices of an equilateral triangle
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)`
A Triangle, in which all sides are equal, is called an equilateral triangle
The given points are `A(2,5),B(8,5),C(5,10.1962)`
`AB=sqrt((8-2)^2+(5-5)^2)`
`=sqrt((6)^2+(0)^2)`
`=sqrt(36+0)`
`=sqrt(36)`
`:. AB=6`
`BC=sqrt((5-8)^2+(10.1962-5)^2)`
`=sqrt((-3)^2+(5.1962)^2)`
`=sqrt(9+27)`
`=sqrt(36)`
`:. BC=6`
`AC=sqrt((5-2)^2+(10.1962-5)^2)`
`=sqrt((3)^2+(5.1962)^2)`
`=sqrt(9+27)`
`=sqrt(36)`
`:. AC=6`
Here `AB=BC=AC`
`:.` ABC is an equilateral triangle
3. Show that the points `A(1,2), B(1,6), C(4.4641,4)` are vertices of an equilateral triangle
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)`
A Triangle, in which all sides are equal, is called an equilateral triangle
The given points are `A(1,2),B(1,6),C(4.4641,4)`
`AB=sqrt((1-1)^2+(6-2)^2)`
`=sqrt((0)^2+(4)^2)`
`=sqrt(0+16)`
`=sqrt(16)`
`:. AB=4`
`BC=sqrt((4.4641-1)^2+(4-6)^2)`
`=sqrt((3.4641)^2+(-2)^2)`
`=sqrt(12+4)`
`=sqrt(16)`
`:. BC=4`
`AC=sqrt((4.4641-1)^2+(4-2)^2)`
`=sqrt((3.4641)^2+(2)^2)`
`=sqrt(12+4)`
`=sqrt(16)`
`:. AC=4`
Here `AB=BC=AC`
`:.` ABC is an equilateral triangle
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
2. Show that the points A(-3,0), B(1,-3), C(4,1) are vertices of a right angle triangle
(Previous example) | 4. Show that the points A(7,10), B(-2,5), C(3,-4) are vertices of an isosceles triangle
(Next example) |
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