{"id":27645,"date":"2020-07-10T18:15:26","date_gmt":"2020-07-10T12:45:26","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=27645"},"modified":"2021-07-02T15:07:05","modified_gmt":"2021-07-02T09:37:05","slug":"kseeb-solutions-for-class-8-maths-chapter-14-additional-questions","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/kseeb-solutions-for-class-8-maths-chapter-14-additional-questions\/","title":{"rendered":"KSEEB Solutions for Class 8 Maths Chapter 14 Introduction of Graphs Additional Questions"},"content":{"rendered":"

Students can Download Maths Chapter 14 Introduction of Graphs Additional Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths<\/a>\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka State Syllabus Class 8 Maths Chapter 14 Introduction of Graphs Additional Questions<\/h2>\n

Question 1.
\nChoose the correct option.
\n(a) The point (4, 0) lie on the line _______
\nA. y – x = 0
\nB. y = 0
\nC. x = 0
\nD. y + x = 0
\nSolution:
\nB. y = 0<\/p>\n

\"KSEEB<\/p>\n

(b) The point (-5, 4) lie in ___________
\nA. the first qudrant
\nB. the second quadrant
\nC. the third quadrant
\nD. the fourth quadrant
\nSolution:
\nB. the second quadrant.<\/p>\n

(c) If a straight pass through (0, 0) and (1, 5) then its equation is ________
\nA. y = x
\nB. y = 5x
\nC. 5y = x
\nD. y = x + 5
\nSolution:
\nC. 5y = x<\/p>\n

(d) If a point P has coordinates (3, 4) in coordinate system X’OX \u2194 Y’OY and if O has coordinates (4, 3) in another system X’1<\/sub>OX1<\/sub>\u00a0\u2194 Y1<\/sub>‘01<\/sub>Y1<\/sub> is __________
\nA. (3, 4)
\nB. (1, -1)
\nC. (7, 7)
\nD. (-1, 1)
\nSolution:
\nC. (7, 7)<\/p>\n

(e) The coordinates of a point P in a system X’OX \u2194 Y’OY are (5, 8). The coordinates of the same point in the system Y’OY \u2194 XOX’ are
\nA. (-8, 5)
\nB. (8, 5)
\nC. (8, -5)
\nD. (-8, -5)
\nSolution:
\nC. (8, -5)<\/p>\n

\"KSEEB<\/p>\n

(f) The signs of the coordinates of a point in the third quadrant are
\nA. (+, -)
\nB. (-, +)
\nC. (+, +)
\nD. (-, -)
\nSolution:
\nD. (-, -)<\/p>\n

(g) If a person moves either 1 unit in the direction of the positive x-axis or 1 unit in the direction of positive y-axis per step; then the number of steps he requires to reach (10, 12) starting from the origin (0, 0) in
\nA. 10
\nB. 12
\nC. 22
\nD. 120
\nSolution:
\nC. 22<\/p>\n

(h) They coordinate of the point of 2. intersection of the line y = 3x + 4 with
\nx = 3 is
\nA. 4
\nB. 7
\nC. 10
\nD. 13
\nSolution:
\nB. 7<\/p>\n

(i) The equation of the line which passes through (0, 0) and (1, 1) is
\nA. y = x
\nB. y = – x
\nC. y = 1
\nD. x = 1
\nSolution:
\nA . v = x<\/p>\n

Question 2.
\nFind the quadrant in which the following points lie.
\nSolution:
\n(i) (5, 10) – I Quadrant
\n(ii) (-8, 9) – II Quadrant
\n(iii) (-800, -3000) – III Quadrant
\n(iv) (8, -100) – IV Quadrant<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nMatch the following
\n(A) on the x axis – (i) x coordinate is negative
\n(B) In th second quadrant – (ii) cuts the y axis at (0, 4)
\n(C) The line y = 3x + 4 – (iii) coordinates of a point are of form (a, 0)
\nSolution:
\n(A) – (iii)
\n(B) – (i)
\n(C) – (ii)<\/p>\n

Question 4.
\nFill in the blanks
\n(a) They coordinate of a point on the x-axis in zero<\/span>.
\n(b) The x coordinate is called abscissa.<\/span>
\n(c) The x-axis and y-axis intersect at (0, 0)<\/span>
\n(d) If a point (x, y) \u2260 (0, 0) is in the third quadrant, then (x + y) has a negative<\/span> sign.
\n(e) If a point (x, y) lies above the horizontal axis, then y is always positive<\/span>.
\n(f) The point of intersection of x = y and x = – y is (0, 0)<\/span>
\n(g) The line y = 4x + 5 intersects y-axis at the point (0, 5)<\/span><\/p>\n

\"KSEEB<\/p>\n

Question 5.
\nTrue or false
\n(a) The equation of the x-axis is x = 0.
\nAnswer:
\nFalse<\/p>\n

(b) The line x = 4 is parallel to the y-axis.
\nAnswer:
\nTrue<\/p>\n

(c) The line y 8 is perpendicular to the x-axis.
\nAnswer:
\nFalse<\/p>\n

(d) The line x = y and x = – y are perpendicular to each other.
\nAnswer:
\nTrue<\/p>\n

(e) The lines x = 9 and y = 9 are perpendicular to each other.
\nAnswer:
\nTrue<\/p>\n

(f) The graph of y = x2 is a straight line.
\nAnswer:
\nFalse<\/p>\n

(g) The line y = 3x + 4 does not in\u00actersect x-axis.
\nAnswer:
\nFalse<\/p>\n

(h) In a rectangular coordinate system, the coordinate axes are chosen such that they form a pair of perpendicular lines.
\nAnswer:
\nTrue<\/p>\n

\"KSEEB<\/p>\n

Question 6.
\nDetermine the equation of the line which passes through the points (0, -8) and (7, 0).
\nSolution:
\nLet the equation be y = ax + b. The line passes through (0, -8). When
\nx = 0 y = – 8
\ny = ax + b
\n– 8 = a (0) + b
\n– 8 = 0 + b
\n\u2234 b = – 8
\nThe lines passes through (7, 0). When x = 7, y = 0
\ny = ax + b
\n0 = a (7) + b, 0 = 7a + b
\n0 = 7a – 8 (\u2234 b = – 8)
\n8 = 7a
\na = \\(\\frac{8}{7}\\)
\ny = ax + b
\ny = \\(\\frac{8}{7}\\) x + (-8)
\n7y = 8x – 56
\n56 = 8x – 7y
\n\u2234 The equation is 8x – 7y = 56<\/p>\n

\"KSEEB<\/p>\n

Question 7.
\nDetermine the equation of the line in each of the following graph.
\n(i)
\n\"KSEEB
\nSolution:
\nFrom the graph we find that the line passes through the points (3, 8) and (-3, -3).
\nLet the equation be y = ax + b
\nWhen x = 3, y = 8
\n\u2234 8 = a (3) + b
\n8 = 3a + b
\n\u2234 b = 8 – 3a
\nWhen x = – 3, y = – 3
\n\u2234 y = ax + b
\n– 3 = a(-3) + b
\n– 3 = – 3a + b
\n– 3 = – 3a + 8 – 3a [\u2234 b = 8 – 3a]
\n6a = 8 + 3
\na = \\(\\frac{11}{6}\\)
\nb = 8 – 3a<\/p>\n

\"KSEEB
\n6y = 11x + 15<\/p>\n

(ii)
\n\"KSEEB
\nFrom the graph we find that the line passes through the points (-4, 2) and (12, -3)
\nLet the equation is y = ax + b
\nWhen x = – 4, y = 2
\n\u22342 = a(-4) + b 2 = – 4a + b
\nb =2+ 4a
\nWhen x = 12, y = – 3, y = ax + b
\n– 3 = a(12) + b – 3 = 12a + b
\n– 3 = 12a + 2 + 4a [\u2234 b = 2 + 4a]
\n– 3 = 16a + 2 – 3 – 2 =16a
\n\"KSEEB
\ny = \\(\\frac{-5 x+12}{16}\\)
\n16y = – 5x + 12
\n16y + 5x + = 12<\/p>\n

\"KSEEB<\/p>\n

Question 8.
\nA point P has coordinates (7, 10) in a coordinate system X’OX \u2194 Y’OY. Suppose it has coordinates (10, 7) in another coordinate system X’1<\/sub>O1<\/sub>X1<\/sub> \u2194 Y’1<\/sub>O1<\/sub>y1<\/sub> with X’OX || X’1<\/sub>O1<\/sub>X1<\/sub>.
\nFind the coordinates of O1<\/sub> in the system X’OX \u2194 Y’OY.
\nSolution:
\nGiven P (x, y) = (7, 10) and (x’, y’) = (10, 7)
\nLet the coordinates of O1 in X’OX – Y”OY be (a, b)
\nx = a + x’ y = b + y’.
\n7 = a + 10
\n10 – b + 7
\n7 – 10 = a
\n10 – 7 = b
\n– 3 = a 3 = b
\na = – 3 b = 3
\n\u2234The coordinates of O1 are (-3, 3)<\/p>\n

Question 9.
\nSketch the region {(x, y) : x > 0, y > 0, x + 2y < 4} in a coordinate system set up by you. Solution: Given x > 0, y > 0 x + 2y < 4
\nLet x = 0 and y = 1, .
\nthen x + 2y = 0 + 2(1) = 0 + 2 = 2 < 4
\nx = 1 and y = 1,
\nthen x + 2y + 1 + 2(1) = 1 + 2 = 3 < 4
\nx = 2 and y = 0, then x + 2y = 2 + 2(0) = 2 + 0 = 2 <4
\nx = 2 and y = 1
\nthen x + 2y = 2 + 2(1) = 2 + 2 = 4
\nx = 0 and y = 0 then x + 2y = 0 + 2(0) = 0 + 0 = 0
\n\"KSEEB
\n\"KSEEB<\/p>\n

\"KSEEB<\/p>\n

Question 10.
\nDraw the graphs of lines 3x = 4x – 4 and 2x = 3y + 4 and determine the point at which these lines meet.
\n\"KSEEB
\nSolution:
\n3y = 4x – 4
\n2x = 3y + 4
\ny = \\(\\frac{4 x-4}{3}\\)
\n2x – 4 = 3y
\ny = \\(\\frac{2 x-4}{3}\\)
\n\"KSEEB<\/p>\n

Question 11.
\nIf a * b = ab + a + b, draw the graph of y = 3 * (x +1) * 2
\n\"KSEEB
\nSolution:
\n3 * (x +1) * 2
\nFind 3 * (x + 1) Given a * b = ab + a + b
\n\u2234 3 * (x + 1) = 3( x + 1) + 3 + (x + 1)
\n= 3x +1 + 3 + x +1
\n3 * (x +1) = 4x + 5
\nNow find 3 * (x +1) * 2
\n= (4x + 5) * 2 = (4x + 5)2 + 4x + 5 + 2
\n= 8x + 10 + 4x + 7
\n3 * (x + 1) * 2 = 12 x + 27
\n\u2234 y = 12x + 27
\nWhen x = – 2, = 12 (-2) + 27
\n= – 12 + 27 – 15
\nWhen x = – 3 y = 12 (-3) + 27
\n= – 36 + 27 = – 9
\n\"KSEEB<\/p>\n

\"KSEEB<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 14 Introduction of Graphs Additional Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka State Syllabus Class 8 Maths Chapter 14 Introduction of Graphs Additional Questions Question 1. Choose the correct …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/27645"}],"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=27645"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/27645\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=27645"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=27645"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=27645"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}