{"id":22527,"date":"2020-02-05T17:19:51","date_gmt":"2020-02-05T11:49:51","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=22527"},"modified":"2021-07-02T15:25:46","modified_gmt":"2021-07-02T09:55:46","slug":"1st-puc-basic-maths-question-bank-chapter-15","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/1st-puc-basic-maths-question-bank-chapter-15\/","title":{"rendered":"1st PUC Basic Maths Question Bank Chapter 15 Co-ordinate System in a plane"},"content":{"rendered":"

Students can Download Basic Maths Chapter 15 Co-ordinate System in a plane Questions and Answers, Notes Pdf, 1st PUC Basic Maths Question Bank with Answers<\/a>\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 1st PUC Basic Maths Question Bank Chapter 15 Co-ordinate System in a plane<\/h2>\n

Question 1.
\nFind the reflection of (-4, 3) through x-axis, y-axis and through the centre.
\nAnswer:
\nReflection through x – axis \u2192 (-4, – 3)
\nReflection through y – axis \u2192 (4,3)
\nReflection through center \u2192 (4, -3)<\/p>\n

Question 2.
\nFind ‘a’ if the distance between the points (a, 2) and (3, 4) is V8 units.
\nAnswer:
\nLet P = (a, 2) and Q = (3, 4)
\nBy data |PQ| = \u221a8
\n\u21d2 \u221a8 = \\(\\sqrt{(3-a)^{2}+(4-2)^{2}}\\)
\n\u21d2 8 = (3 – a)2<\/sup> + 22<\/sup> = 8
\n\u21d2\u00a09 + a2<\/sup> – 6a + 4
\n\u21d2 a2<\/sup> – 6a + 5 = 0
\n\u21d2 (a – 5)(a – 1) = 0
\n\u21d2 a = 5 or a = 1<\/p>\n

\"1st<\/p>\n

Question 3.
\nShow that the points (2, 2) (6, 3) and (4,11) form a right angled triangle.
\nAnswer:
\nLet A = (2, 2), B = (6, 3), C = (4, 1)
\nConsider
\n\"1st
\nBy pythagorus theorem AC2<\/sup> = AB2<\/sup> + BC2<\/sup>
\n\"1st
\n\u21d2 85 = 17 + 68 = 85
\n\u2234 the points form a right angled triangle.<\/p>\n

Question 4.
\nThe points (x, 2) is equidistant from (8, -2) and (2, -2). Find the value of x.
\nAnswer:
\nLet A = (2,2) B = (8,-2) C = (2,-2)
\nBy data AB = AC = AB2<\/sup> = AC2<\/sup>
\n\u21d2 (8 – x)2<\/sup> + (-2 -2)2<\/sup> = (x – 2)2<\/sup> + (2 + 2)2<\/sup>
\n\"1st
\n-16x + 4x = 4 -64 \u21d2 – 12x = -60
\n\u2234 x = 5<\/p>\n

\"1st<\/p>\n

Question 5.
\nIf two vertices of an equilateral triangle are (3,4) and (-2,3). Find the co-ordinates of third vertex.
\nAnswer:
\nLet A = (3, 4), B = (-2, 3) and C = (x, y)
\nbydata AB = BC = CA
\n\u21d2 AB2<\/sup> = BC2<\/sup> = CA2<\/sup>
\nconsider BC2<\/sup> = CA2<\/sup>
\n\u21d2 (x + 2)2<\/sup> + (y – 3)2<\/sup> = (x – 3)2<\/sup> + (y – 4)2<\/sup>
\n\"1st
\n4x + 6x – 6y + 8y = 25 – 13
\n\u2234 10x + 2y =12
\n5x + y = 6 …… (1)
\nAgain AB = BC
\n\u21d2 AB2<\/sup> = BC2<\/sup>
\n\u2234 5(3 + 2)2<\/sup> + (4 – 3)2<\/sup> = (x + 2)2<\/sup> + (y – 3)2<\/sup> ………. (2)
\nfrom(1) y = 6 – 5x
\n\u2234 substitute (1) is (2)
\n(x + 2)2<\/sup> + (6 – 5x – 3)2<\/sup> = 26
\nx2<\/sup> + 4 + 4x + 9 + 25x2<\/sup> – 30x = 26
\n26x2<\/sup> – 26x – 13 = 0
\n\u21d2 2x2<\/sup> – 2x – 1 = 0
\n\"1st<\/p>\n

\"1st<\/p>\n

Section Formula<\/span><\/p>\n

Question 1.
\nFind the co-ordinates of the point which divide the line joining the points
\n(i) (1, -3) and (-3, 9) internally in the ratio 1 : 3 and the line joining the points
\n(ii) (2, -6) (4, 3) externally is the ratio 3 : 2.
\nAnswer:
\n(i) Let A = (1, -3) B = (-3 9), Ratio is 1 : 3
\n\"1st<\/p>\n

(ii) Let A = (2, -6) B = (4, 3) ratio 3 : 2
\n\"1st<\/p>\n

Question 2.
\nFind the ratio in which (2, 7) divides the line joining the point (8, 9) and (-7, 4).
\nAnswer:
\nLet
\nA = (x1<\/sub> y1<\/sub>) = (8, 9)
\nB = (x2<\/sub> y2<\/sub>) = (-7, 4)
\np = (x1<\/sub> y2<\/sub>) = (2, 7)
\nThe ratio l : m in which p divides AB, is given by
\n\"1st
\n\u21d2 The ratio is l : m = 2 : 3
\n\u2234 the points (2,7) divides internally<\/p>\n

\"1st<\/p>\n

Question 3.
\nDetermine the ratio in which the line 3x + y – 9 = 0 divide the segment joining the points (1, 3) and (2, 7).
\nAnswer:
\nLet the of division k : 1 as and point then the coordinates of the points are \\(\\left(\\frac{2 k+1}{k+1}, \\frac{7 k+3}{k+1}\\right)\\)
\nBut the point ‘C’ lies on 3x + y – 9 = 0
\n\"1st
\n\u21d2 4x – 3 = 0
\n\u21d2 k = \\(\\frac { 3 }{ 4 }\\)
\n\u2234 The required ratio is 3 : 4 internally<\/p>\n

Question 4.
\nFind the lengths of the medians of a triangle whose vertices are (3, 5) (5, 3) and (7, 7).
\nAnswer:
\nMedian is a tine joining the vertex of a triangle to the middle points of the opposite side.
\nLet A(3, 5) B(5, 3) C(7, 7) the vertices
\nLet D, E, F be the mid points of BC, CA, AB respectively
\n\"1st
\n\"1st<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Basic Maths Chapter 15 Co-ordinate System in a plane Questions and Answers, Notes Pdf, 1st PUC Basic Maths Question Bank with Answers\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 1st PUC Basic Maths Question Bank Chapter 15 Co-ordinate System in a plane …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[81],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/22527"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=22527"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/22527\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=22527"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=22527"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=22527"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}