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Class 10 Difference between two points and section formula Worksheets

1.

Find the ratio in which the line segment joining the point A(3,-3) and B(-2,7) is divided by x axis. Also find the coordinates of the point of division.

2.

The coordinates of the vertices of triangle PQR are P(7,2), Q(9,10) and R(1,4). If E & F are the mid point of PQ and PR, prove that EF= 1/2 QR.

3.

If the distance of P(x,4) from A(6,2) and B(-2,6) are equal prove that y=2x.

4.

If the coordinate of point P on the line segment joining A(1,2) and B(6,7) such that AP = 2/5 AB.

5.

If the coordinates of points A and B are (-2,-2) and (2,-4) find the coordinates of P such that AP = 3/7 AB, where P lies on the line segment AB.

6.

Point A lies on the line segment PQ joining P(6,-6) and Q (-4,-1) in such a way that PA/PQ = 2/5. If point P also lies on the line 3x + K (y+1) = 0. Find the value of k.

7.

Show that the points (a,a) (-a,-a) and are the vertices of an equilateral triangle.

8.

If the point C(-1, 2) divides internally the line segment joining the points A(2,5) and B(x,4) in the ratio 3:4. Find the value of

9.

If the vertices of ABC are A(5,-1), B(-3,-2), and C(-1,8), find the length if median through A.

10.

If (3,2) and (-3,2) are two vertices of an equilateral triangle which contains the origin, find the third vertex.

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