Question

II. ANSWER ALL THE FOLLOWING:
15x6-30
11. If A={1,2,3,4},B={3,4,5) and C={3,5,6,7} then verify
Ax(BUC)={A.B} {AIC}.
12. Iff:R → R is defined by f(1) = 41+5, Prove that f is one-one and onto.
13. Prove that the points (3,4), (6,8), (9,8) and (6,4) form a parallelogram.
14. Find the value of K if the lines
(1) 3x+2y+1=0 and Kx+2y-1=0 are parallel,
(ii) 51-4y+8=0 and 41+Ky+3=0 are perpendicular.
15. Find the equation of the straight line which is passing through the
intersection of the lines 2x-3y-+=0 and 2x+2y-1=0 and perpendicular to the
line +4y-8=0.
16. If a vertex of a triangle is (1.1) and the midpoints of two sides through this
vertex are (-1.2) and (3,2) then find the centroid of the triangle.
17. The angle between two lines is and the slope of one line is Find the
slope of the other line.
18. Find the point of intersection of the straight lines 31-45-1=0 and 5x-7x-1=0.​

Answer 1

In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

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