#### Term 3 Coordinate Geometry Two Marks Questions

9th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 20
10 x 2 = 20
1. If the mid-point (x,y) of the line joining (3,4) and (p,7) lies on 2x + 2y +1 = 0 , then what will be the value of p?

2. The mid-point of the sides of a triangle are (2,4), (−2,3) and (5,2). Find the coordinates of the vertices of the triangle.

3. A(−3,2) , B(3,2) and C(−3,−2) are the vertices of the right triangle, right angled at A. Show that the mid-point of the hypotenuse is equidistant from the vertices.

4. Show that the line segment joining the mid-points of two sides of a triangle is half of the third side
(Hint: Place triangle ABC in a clever way such that A is (0,0), B is (2a,0) and C to be (2b,2c). Now consider the line segment joining the mid-points of AC and BC. This will make calculations simpler).

5. The vertices of a triangle are (1,2), (h,−3) and (−4,k). If the centroid of the triangle is at the point (5,−1) then find the value of $\sqrt { { (h+k) }^{ 2 }+{ (h+3) }^{ 2 } }$

6. ABC is a triangle whose vertices are A(3,4), B(−2,−1) and C(5,3) . If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D.

7. If  $\left( \frac { 3 }{ 2 } ,5 \right) ,\left( 7,\frac { -9 }{ 2 } \right)$and$(\frac{13}{2},\frac{-13}{2})$ are mid-points of the sides of a triangle, then find the centroid of the triangle.

8. Using section formula, show that the points A (7, -5), B (9, -3) and C (13, 1), are collinear.

9. A car travels, at an uniform speed. At 2pm it is at a distance of 5 km at 6pm it is at a distance of 120 km. Using section formula, find at what distance it will reach 2 midnight.

10. Find the centroid of the triangle whose vertices are (2, -5), (5, 11) and (9,9)