Coordinate Geometry

Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!

1. The distance between the points

A (10 \cos θ, 0)

and

B (0, 10 \sin θ)

is .
2. The perimeter of the triangle formed by the points O(0, 0), A(a, 0) and B(0, b) is

\frac{1}{2}

.
3. The ratio in which the line segment joining points (2, 3) and (3, - 2) is divided by X axis is : .
4. The distance between the points

(5 \sin 60 °, 0)

and

(0, 5 \sin 30 °)

is .
5. If A(- 1, 3), B(1, - 1) and C(5, 1) are vertices of a triangle ABC, then the length of the median through vertex A is .
6. The distance between points (x, 0) and (0, 3) is 5, the values of x is

\pm

.
7. The area of the triangle formed by the points O(0, 0), A(6, 0) and B(0, 4) is square units.
8. If the centroid of the triangle formed by points P(a, b), Q(b, c) and R(c, a) is at the origin, the value of a + b + c is .
9. If the centroid of the triangle formed by points P(a, b), Q(b, c) and R(c, a) is at the origin, the value of

\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b}

is .
10. If the mid-point of the segments joining A(x, y + 1) and B(x + 1, y + 2) is

C (\frac{3}{2}, \frac{5}{2})

, then x = , y = .

Coordinate Geometry

Gap-fill exercise