The Total solution for NCERT class 6-12
If the line segmentjoining the points P(x1,y1) and Q(x2, y2) subtends an angle α at the origin O, prove that: OP. OQ cos α = x1 x2 + y1 y2.
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