Show that the points (8,4),(5,7),(-1,1),(2,-2)[taken in order] form a rectangle.
Show that the points (8,4),(5,7),(-1,1),(2,-2)[taken in order] form a rectangle.
Drovan Reddy , 9 Years ago
Grade 9
Analytical Geometry> Show that the points (8,4),(5,7),(-1,1),(...
2 Answers
Saurabh Koranglekar
Last Activity: 5 Years ago
Vikas TU
Last Activity: 5 Years ago
Dear student
Opposite sides of rectangle are congruent
d (P, Q)=
sqrt{(8 - 2)^{2} } + sqrt{(4 + 2}^{2}
d (P, Q)=
sqrt{(8 - 2)^{2} } + sqrt{(4 + 2}^{2}
=
sqrt{36 + 36}
sqrt{36 + 36}
=
sqrt{72}
=
sqrt{8 \times 9}
sqrt{8 \times 9}
=
3 sqrt{8}
similarly, d (Q, R), d (R, S)and d (P, S) will be
3 sqrt{8}
Hence points P, Q, R and S form a rectangle
Provide a better Answer & Earn Cool Goodies
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Other Related Questions on analytical geometry
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
analytical geometry
0 Answer Available
Last Activity: 2 Years ago
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
0 Answer Available
Last Activity: 2 Years ago
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
analytical geometry
0 Answer Available
Last Activity: 2 Years ago
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
analytical geometry
0 Answer Available
Last Activity: 3 Years ago
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
0 Answer Available
Last Activity: 3 Years ago