- 12. Find the distance between the points A(-4, 7) and B(2, -5).

A.) 8√5 Units B.) 6√5 Units C.) 6√4 Units D.) None of these Answer: Option 'B'

AB = √(2+4)^{2}+ (-5-7)^{2}

= √6^{2}+ (-12)^{2}

= √36+144 = √180

=√36*5 = 6√5 units. - 13. The distance between the points A(b, 0) and B(0, a) is.

A.) √a ^{2}-b^{2}B.) √a ^{2}+b^{2}C.) √a+b D.) a-b Answer: Option 'B'

AB = √(b-0)^{2}-(0-a)^{2}

= √b^{2}+a^{2}

= √a^{2}+b^{2}. - 14. If the distance of the point P(x, y) from A(a, 0) is a + x, then y
^{2}= ?

A.) 8ax B.) 6ax C.) 4ax D.) 2ax Answer: Option 'C'

√(x-a)^{2}+(y-0)^{2}= a + x

= (x-a)^{2}+y^{2}

= (a+x)^{2}=> y^{2}= (x-a)^{2}-(x-a)^{2}-4ax => y^{2}= 4ax - 15. The distance between the points A(5, -7) and B(2, 3) is:

A.) 109 B.) 5√7 C.) √109 D.) None of these Answer: Option 'C'

AB^{2}= (2 - 5)^{2}+ (3 + 7)^{2}

=> (-3)^{2}+ (10)^{2}

=> 9 + 100 => √109

If (x_{1}, y_{1}) and B(x_{2}, y_{2}) be two points, then

AB = √(x_{2}- x_{1})^{2}+ (y_{2}- y_{1})^{2}

Students can learn and improve on their Cognitive and Mathematical Fast Calculation skills and prepare for competitive examinations like...

- All I.B.P.S and Public Sector Bank Competitive Exam
- Common Aptitude Test (CAT) Exams
- UPSC Paper-II or CSAT Exams
- SSC Competitive Exams
- Defence Competitive Exams
- L.I.C / G.I.C AO and Clerk Competitive Exams
- Railway Competitive Exam
- University Grants Commission (UGC)
- Career Aptitude Test (IT Companies) and etc.

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