Show that the following points are collinear.
A(5,1),B(1,−1) and C(11,4).
The three points (−2,2)(9,−2),and(−4,−3) are the vertices of (a) an isosceles triangle (b) an equilateral triangle (c) a right-angled triangle (d) none of these
In a classroom, 4 friends are seated at the points A. B. C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, Don't you think ABCD is a square? Chameli disagrees. Using distance formula, find which of them is correct.
If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle POR is (are) always rational point(s) ?
Let A(2,−3)andB(−2,1) be the vertices of ABC˙ If the centroid of the triangle moves on the line 2x+3y=1, then find the locus of the vertex C˙
If Q(0, 1) is equidistant from P(5, 3)and R(x, 6), find the values of x. Also find the distances QR and PR.
If x1,x2,x3 as well as y1,y2,y3 are in GP with the same common ratio, then the points (x1,y1),(x2,y2), and (x3,y3)˙ lie on a straight line lie on an ellipse lie on a circle (d) are the vertices of a triangle.
The line joining A(bcosαbsinα) and B(acosβ,asinβ) is produced to the point M(x,y) so that AM and BM are in the ratio b:a˙ Then prove that x+ytan(α+2β)=0.