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Coordinate Geometry

Short Answer Type

361. Find the number of terms in the

straight A. space straight P. space colon space minus 1 comma space fraction numerator negative 5 over denominator 6 end fraction comma space fraction numerator negative 2 over denominator 3 end fraction comma space fraction numerator negative 1 over denominator 2 end fraction comma space..... comma space 10 over 3.

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362.

Two A .P’s have the same common difference. The first term of these is 3 and that of the order is 8. What is the difference between their

(i) 2nd terms (ii) 4th terms (iii) 10th terms (iv) 30th terms.

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363. The fourth term of an A .P. is equal to 3 times the first term and the 7th term exceeds twice the third term by 1. Find the 1st term of A .P.

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364. If eight times the 8th term of an A .P. is equal to 12 times the 12th term of the A .P., then find the 20th term.

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365.

Find :

(i) The 10th term of –40, –15, 10, 35,.........

(ii) The 9th term of $3 over 4 comma space 5 over 4 comma space 7 over 4 comma space 9 over 4 space.......$

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366. If (n + 1), 3n and (4n + 2) are in A .P., find the value of ‘n’.

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367. The 51 st, 11 th and last terms of an A .P. arc 0, 8 and

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respectively. Find the common difference and the number of terms.

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368.

Let P and Q be the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4) such that P is nearer to A. Find the coordinates of P and Q.

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369.

Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.

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370.
If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b,a + b). Prove that bx = ay.

Given,

P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b,a + b)
Since P is at equidistant
therefore,
AP=BP
Thus using section formula
$square root of left square bracket straight x minus left parenthesis straight a plus straight b right parenthesis squared right square bracket plus left square bracket straight y minus left parenthesis straight b minus straight a right parenthesis squared right square bracket end root space equals space square root of left square bracket straight x minus left parenthesis straight a minus straight b right parenthesis right square bracket squared plus left square bracket straight y minus left parenthesis straight a plus straight b right parenthesis right square bracket squared end root left square bracket straight x minus left parenthesis straight a plus straight b right parenthesis right square bracket squared plus left square bracket straight y minus left parenthesis straight b minus straight a right parenthesis right square bracket squared space equals left square bracket straight x minus left parenthesis straight a minus straight b right parenthesis right square bracket squared plus left square bracket straight y minus left parenthesis straight a plus straight b right parenthesis right square bracket squared straight x squared minus 2 straight x left parenthesis straight a plus straight b right parenthesis plus left parenthesis straight a plus straight b right parenthesis squared plus straight y squared minus 2 straight y left parenthesis straight b minus straight a right parenthesis plus left parenthesis straight b minus straight a right parenthesis squared equals straight x squared minus 2 straight x left parenthesis straight a minus straight b right parenthesis plus left parenthesis straight a minus straight b right parenthesis squared plus straight y squared minus 2 straight y left parenthesis straight a plus straight b right parenthesis plus left parenthesis straight a plus straight b right parenthesis squared minus 2 straight x space left parenthesis straight a plus straight b right parenthesis minus 2 straight y space left parenthesis straight b minus straight a right parenthesis space equals negative 2 straight x space left parenthesis straight a minus straight b right parenthesis minus 2 straight y left parenthesis straight a plus straight b right parenthesis ax plus bx plus by minus ay equals ax minus bx plus ay plus by 2 bx equals 2 ay bx equals ay$

Hence proved.

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

370. If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b,a + b). Prove that bx = ay.

370.
If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b,a + b). Prove that bx = ay.