Question

1. Find the coordinates of the mid point of the line segment joining the points (4,3) and (2, 1).
2. Find the coordinates of the point which divides the line segment joining the points (1,3)
and (2, 7) in the ratio 3: 4.
3. Show that the points (1, 1), (3, -2) and (- 1,4) are collinear.
4. Find the centroid of the triangle whose vertices are (3.-5); (-7.4) and (10,-2).
5. If the distance of the point P(x, y) from the points A (5, 1) and B (-1,5) is equal, show that
3x = 2y.
6. Find the area of a triangle whose vertices are A (1, 2); B (3,5) and C (-4, - 7).
7. In what ratio does the point P (-4, 6) divide the line segment joining the points A (-6, 10)
and B (3,-8).
8. For what value of m, the points (4,3), (m. 1) and (1,9) are collinear.

Answer 1

Answer:

1.(3,2)

2.(11/7,37/7)

Step-by-step explanation:

1. Co-ordinates of the mid point

= ((4+2)/2 , (3+1)/2)

= (6/2 , 4/2)

= (3 , 2)

2. co-ordinates of the point dividing the (1,3) and ( 2 ,7) in the ratio of 3:4 are

((m×x1+n×x2)/(m+n),(m×y1+n×y2)/(m+n))

= ((3×1+4×2)/(3+4),(3×3+4×7)/(3+4))

=((3+8)/7,(9+28)/7)

= (11/7,37/7)