Q. 4 E5.0( 2 Votes )

# Show that the fol

Answer :

Formula used: (5, 9), (5, 16) and (29, 9)

Let the points be A (5, 16), B (5, 9) and C (29, 9)

Distance of AB

AB = √ ((5 – 5)2 + (9 – 16)2)

AB = √ ((0)2 + (–7)2)

AB = √ (0 + 49)

AB = √49

Distance of BC

B C= √ ((29 – 5)2 + (9 – 9)2)

BC = √ ((24)2 + (0)2)

BC = √ (576 + 0)

BC = √576

Distance of AC

AC = √ ((29 – 5)2 + (9 – 16))2)

AC = √ ((24)2 + (–7)2)

AC = √ (576 + 49)

AC = √ 625

i.e. AB2 + BC2

= (√49)2 + (√576)2

= 49 + 576

= 625 = (AC)2

Hence, ABC is a right–angled triangle. Since the square of one side is equal to sum of the squares of the other two sides.

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