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Coordinates of Points and Distances

Question 7Any...

Question

Question 7
Any point on the x-axis is of the form:

A) (x, y)
B) (0, y)
C) (x, 0)
D) (x, -y)

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Solution

The answer is C.
Every point on the X-axis has its y-coordinate equal to zero i.e., y = 0.
Hence, the general form of every point on X-axis is (x, 0).

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f

g

[0, a]

f (x) = f (a - x)

g (x) + g (a - x) = 4,

a \int 0 f (x) g (x) d x

\int_{0}^{2 a} f (x) = d x = \int_{0}^{a} f (x) d x + \int_{0}^{a} f (2 a - x) d x

Any point on x- axis is in the form (a, 0).

List I	List II
I. $\int_{- 1}^{1} x \| x \| d x$	(a) $\frac{π}{2}$
II. $\int_{0}^{\frac{π}{2}} (1 + log (\frac{4 + 3 sin x}{4 + 3 cos x})) d x$	(b) $\int_{0}^{\frac{a}{2}} f (x) d x$
III. $\int_{0}^{a} f (x) d x$	(c) $\int_{0}^{a} [f (x) + f (- x)] d x$
IV. $\int_{- a}^{a} f (x) d x$	(d) $0$
	(e) $\int_{0}^{a} f (a - x) d x$

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