A(2,3), B(4,7)and C(6,11) are three points in a plane. Choose the correct statement.
A, B and C are collinear
Three points are collinear if the slope of AB equals the slope of BC.
Slope of AB = \(\frac{7 - 3}{4 - 2} = \frac{4}{2} = 2\)
Slope of BC = \(\frac{11 - 7}{6 - 4} = \frac{4}{2} = 2\)
Both slopes are equal and B is a common point, so A, B and C lie on the same straight line. They cannot form a triangle.
Hence, the answer is A, B and C are collinear.
A line passes through the point (4,3) and intercepts the x-axis at 8. Find its y-intercept.
The midpoint of a line segment joining two points P(-14, 4) and Q(2, -4) is:
The point P(4,5) divides AB internally in the ratio 1:1, where A(2,3) and B(x,y). What are the coordinates (x,y)?
In which ratio the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3)?
In which quadrant both abscissa and ordinate are negative?
Find the slope of the line joining the points (3, -4) and (5, 2).
A1 (x1, y1), A2 (x2, y2), A3 (x3, y3) and A4 (x4, y4) are 4 points, p1 divides A1A2 in the ratio 1 ∶ 1, p2 divides P1A3 in the ratio 1 ∶ 2, P3 divides p2A4 in the ratio 1 ∶ 3. Then the coordinates of p3 are:
The polar coordinates of the vertices of a triangle are (0, 0), \(\left( {3,\frac{\pi }{2}} \right)\) and \(\left( {3,\frac{\pi }{6}} \right)\). Then, the triangle is: