If the line segmentjoining the points P(x_{1},y_{1}) and Q(x_{2}, y_{2}) subtends an angle α at the origin O, prove that: OP. OQ cos α = x_{1} x_{2} + y_{1} y_{2}.

Answer 1 :

Given,

Two points P and Q subtends an angle α at the origin as shown infigure:

From figure we can see that points O, P and Q forms a triangle.

Clearly in ΔOPQ we have:

Answer 2 :

Given:

The coordinates of triangle.

From the figure,

By using cosine formula,

In ΔABC, we have:

Four points A (6,3), B (-3, 5), C (4, -2) and D (x, 3x) are given in such a way that , find x.

Answer 3 :

24.5 = 28x – 14

28x = 38.5

x = 38.5/28

= 1.375

The points A (2,0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD.Determine whether ABCD is a rhombus or not.

Answer 4 :

The coordinates of 4 points that form a quadrilateral is shownin the below figure

Now by using distance formula, we have:

It is clear that, AB ≠ BC [quad ABCD does not have all 4sides equal.]

∴ ABCDis not a Rhombus

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