Chapter 6 Coordinate Geometry
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Question 1 : The vertices of a triangle are P (6, 1), Q (5, 6) and R (m, -1). Given that the area of the triangle is 31 unit 2 , find the values of m. Question 2 : The points P (3m, m), Q (t, u) and R (3t, 2u) lie on a straight line. Q divides PR in the ratio 3: 2. Express t in terms of u. Question 3 : The equation of the straight lines CD and EF are 5x + y – 4 = 0 and x 7 − y h =1 . If CD and EF are parallel, find the value of h. Question 4 : The straight line x 5 + y p =1 has a y-intercept of 3 and is parallel to the straight line y + qx= 0. Determine the value of p and of q. Question 5 : The equations of two straight lines y 7 + x 4 =1 and 7y = 4x + 21. Determine whether the lines are perpendicular to each other. Question 6 : The point M is (–3, 5) and the point N is (4, 7). The point P moves such that PM: PN = 2: 3. Find the equation of the locus of P. Question 7 :
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Coordinate Geometry
Transcript of Chapter 6 Coordinate Geometry
Question 1:The vertices of a triangle areP(6, 1),Q(5, 6) andR(m, -1). Given that the area of the triangle is 31 unit2, find the values ofm. Question 2:The pointsP(3m,m),Q(t, u) andR(3t, 2u) lie on a straight line.QdividesPRin the ratio 3: 2. Expresstin terms ofu.
Question 3:The equation of the straight linesCDandEFare 5x+y 4 = 0 and . IfCDand EFare parallel, find the value ofh.
Question 4:The straight line + =1has ay-intercept of 3 and is parallel to the straight liney+qx= 0. Determine the value ofpand ofq.
Question 5:The equations of two straight lines + =1and 7y= 4x+ 21. Determine whether the lines are perpendicular to each other.
Question 6:The pointMis (3, 5) and the pointNis (4, 7). The pointPmoves such thatPM:PN= 2: 3. Find the equation of the locus ofP.
Question 7:Given the pointsA(0, 2) andB(6, 5). Find the equation of the locus of a moving pointP such that the triangleAPBalways has a right angle atP.
Question 1:
The diagram shows a straight linePQwhich meets a straight lineRSat the pointQ. The pointPlies on they-axis.(a)Write down the equation of RS in the intercept form.(b)Given that 2RQ=QS, find the coordinates ofQ.(c)Given thatPQis perpendicular toRS, find they-intercept ofPQ.
Question 2:
The diagram shows a trapeziumPQRS. Given the equation ofPQis 2yx 5 = 0, find(a)The value ofw,(b)the equation ofPSand hence find the coordinates ofP.(c)The locus ofMsuch that triangleQMSis always perpendicular atM.
Question 3:
In the diagram,PRSandQRTare straight lines. GivenRis the midpoint ofPSandQR : RT= 1 : 3, Find(a)the coordinates ofR,(b)the coordinates ofT,(c)the coordinates of the point of intersection between linesPQandSTproduced.Question 4:
The diagram shows a triangleLMNwhereLis on they-axis. The equation of the straight lineLKNandMKare 2y 3x+ 6 = 0 and 3y+x 13 = 0 respectively. Find(a)the coordinates ofK(b)the ratioLK:KN
Question 5:
In the diagram, the equation ofFMGisy= 4. A pointPmoves such that its distance from Eis always half of the distance ofEfrom the straight lineFG. Find(a)The equation of the locus ofP,(b)Thex-coordinate of the point of intersection of the locus and thex-axis.
Question 6:Diagram below shows a triangleOPQ. PointSlies on the linePQ.
(a)A pointYmoves such that its distance from pointSis always 5 uints. Find the equation of the locus ofY.(b)It is given that pointPand pointQlie on the locus ofY . Calculate (i)the value ofk, (ii)the coordinates ofQ.(c)Hence, find the area, in uint2, of triangleOPQ.
