Find the distance of the following points from the origin:
A train travels at a certain average speed for a distance of 54 km and then travels a distanceof 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours tocomplete the total journey, what is its first speed?
If P(2a,4) is the mid-point of the line-segment joining the pointsA(−6,5)andB(−2,3), then the value of a is
Write the answer of each of the following questions:
(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
(ii) What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines intersect.
Let A(4,2),B(6,5) and C(1,4) be the vertices of ΔABC.
(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP:PD=2:1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ:QE=2:1 and CR:RF=2:1.
(iv) What do yo observe?
[Note : The point which is common to all the three medians is called the centroid and this point divides each median in the ratio 2:1.]
(v) If A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of ΔABC, find the coordinates of the centroid of the triangle.
In what ratio does the point (1124,y) divide the line segment joining thepoints P(2, 2) and Q(3, 7) ? Also find the value of y.