ChapterIIIrevisionmathsHabtom

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BERHAN COMPUTER AND TUTORIAL CLASS CHAPTER III) 1.If (a , b) is a point which lies on the third quadrant .In which quadrant does the following points lie: a. (b ,a)____ b.(a 2 ,b)___ c.(-a, -b) ___ d. (a 2 , b 3 ) e.(ab, a+b)__ 2. If (a ,b) lies in the 2 nd quadrant then in which quadrant does the point (-a+b ,ab) belong: 4. Find the coordinates of the midpoints of the line segment with the following end points: a.(-5,4) and (3,2) =___ b.(-4,-3) and (3,4) =__c.(-1/2, -3) and (9,-3) =____ d. (-2,4) andorigin=______ e.(0,-7) and (-7,0) =____ f.(a,-b) and (2a,2b) = ____ 5.The midpoint of a line segment has coordinates (2,-3).one end point of the segment is at(3,-4). Then the coordinates of the other end point is: 6.Which of the following vertices of a triangle are not the vertices of isosceles triangle: a. (2,3),(5,7),(1,4) b. (1,0),(0,5),(5,4) c.( 7,-1),(2,-2),(3,3) d. (4,-7),(-3,-4),(7,0) e. none 7.Find the distance between the following points: a. (1,3) and (4,7) ________ b. (-2,-3) and (1,10)____ c. (5,-12) and (0,0)___ d. (2,-1) and(-1,2)________ e. (a,-b) and (2a,2b) _____ f. (-5,5)and(2,-3)_________ 8. Find the value of x , if the distance between the point (x,-1) and (3,2) is 5 units: 9.What kind of triangle has the vertices A(1,1) B(-1,-1) C(-√3, √3) 10. What kind of triangle has the vertices A(0,6) B(-5,3) C(3, 1) 11.What kind of quadrilateral has the following vertices taken in order? A(1,1) B(5,3) C(7,7) D(3,5) b. A(4,7) B(0,4) C(3,0) D(7,3) c. P(1,0) Q(3,-6) R(8,1) S(6,7) d. F(-2,0) G(0,4) H(6,0) I(0,-4) e. V(3,2) W(0,5) X(-3,2) Y(0,-1) f. K(-7,2) M(-2,5) N(1,2) O(-4,-1) P(2,-1) Q(3, 4), R(-2,3) and S(-3, -2)taken in order are the vertices of a rhombus but not a square. 12.The coordinates of the point that divides the line segment with end points (5,-2)and (9,6) in the ratio 3:1 is 13. In what ratio does the point P(-3,7) divide the line segment with end points X(-5,18) and Y(4,-7) ? 14. The point (3,3) divides the line segment with endpoints (-5,-1) and (7,5) in the rati 15. If P(-4,3) divides the line segment with AB in the ratio 3:4 internally. If A(-1,-3)then coordinates of B are 16.The ratio in which the X-axis divides the line segment with end points (4,5) and (-10,-2) is: 17.The coordinates of the two trisection points of the line segment joining P 1 (-5,2) and P 2 (7,4): 18.Find the slope of a line passing through the following points: a.(2,3),(9,12) b.(-5,9),(-5,-6) c.(1,-2),(-2,1) d.(-2,-6), (2,1) e. (a, b),(b ,a) f.(a, b),(-a,-b) g. (a+1,b-2),(a-1,b+2) 19. Determine the slope of the lines with the following equations: a.4x+3y=9 b. 3y+5x -7=0 c. 3y=4 d. 4x+1=0 e. 2y-x-4=0 f.5y-6x=15 g. ax+ by +c=0 20.Which of the following lines passes through (-3,2): a.2x -y+8=0 b.x+3y-6=0 c.5x-4y+20=0 d.4x+7y-2=0 e. none 21.Find the value of x so that the line passing through (-2,4) and (x,-4) will have no slope: 22.Which of the following points are not collinear : a.(-3,3), (2,1),(12,-3) b.(2,1),(-1,2),(5,0) c.(1,3),(-2,-4),(3,-2) d. (-1,-2),(6,-5),(20,-11) 23.Determine the equation of the line with the given slope and passing through the given point: a. m=5/2 ;( -2,-3) b. m= -1/2 ; (3,4) c. m=0; (6,-6) d. m=6; (-5,2) e. m=-2 ; (3,-4) f. no slope ; (-1,-3) 24. The equation of the line passing through the coordinates (3,5) and(1,4)is given by: a. y-2x-7=0 b. 2y-x-7=0 c. 2y+x+7=0 d. y+2x-7=0 e. none 25. Determine the equation of the line passing through the following points : a.(4,6),(1,-3) b.(-2,-4),(1,-3) c. (0,32),(100,212) d.(-1, 3/4),(-1/2, 2) e.(1,0),(0,1) f.(2,-3),(2,-4) 26. If the point (x,3) is equidistant from (3,-2) and (7,4) then the value of X is: 27. Which point on the y-axis is equidistant from (2, 3) and (-4,1) : 28. The length of the median from A in ABC with coordinates A(5,7) ,B(-3,5) C(5,3) 29.In ABC ,D(4,3) is the midpoint of AB, E(5,6) is the midpoint of BC and F(1,2) is the midpoint of AC .Find the coordinates of A=______, B=________ and C =_______ 30-.Find the distance between the given line and the given points. a. 6x-2y+7=0 ; (4,1) b. x+2y-4=0 ; (0,-3) c.3x+y=-4 ; (-4,-4) d. x=-y ; (4,-1) e.4x-3y=15 ; (4,1) f. x=3 ; (2,-5) 31. The points A(1,2) B(5,2) and C(3,4) form the vertices of a triangle. The slope of the altitude from A is: 32.The equation of a line is Y= -2x+b.For what value of b line the line pass through (1,3) 33.The slope of a line which is perpendicular to the line which passes through (-3,2) and (-1,-4 34.Which of the following lines is not parallel to the line with the equation x-2y+6=0? a. 2x-4y=3 b. 2y-x+7=0 c.4x-2y+9=0 d.6y-3x-5=0 e. none 35.The equation of a line parallel to the line 3x+4y-10=0 and passing through (-4,-3) is: 36.The equation of a line which passes through (2,-1) and perpendicular to 3x-y+2=0 is:
BERHAN COMPUTER AND TUTORIAL CLASS 37. The equation of the line perpendicular to the line 5x + 3 = o and passing through the point (-2,3) is : 38. the equation of the line parallel to the line with equation 7y -5= 0 and passing through (-8,5) is: 39.If the vertices of a triangle are A(1,1) B(5,2) C(3,4),then the slope of the altitude to point BC is: 40.If the vertices of ∆ABC are A(-1,2) B(5,0) C(1,8) ,then the slope of the median from B 41.If the vertices of a triangle are A(5,5) B(3,0)C(-1,2).then the equation of the median from A is: 42.The equation of the perpendicular bisector of the line segment joining (2,3) and (-4,5) is 43.The vertices of a triangle are A(-2,4) B(6,10) C(4,6) a. find the equation of the median from C is : b.the equation of the perpendicular bisector of AC c. the equation of the altitude to BC 44.The equation of perpendicular bisector of the line segment with end points A(-1,3) and B(5,-1)is: 45.In ∆ABC with vertices A(12,4) B(1,1) C(0,8) find A. the point of intersection of the three medians. B. the point of intersection of the three altitudes C. the point of intersections of the three perpendicular bisectors 46. For what value of K is the line 2x-Ky+5=0 is parallel to the line 8x-14y+3=0. a.2/7 b.4/7 c. -7/2 d.7/2 e. none 47. For what value of K is the line 4x+ky-8=0 is perpendicular to the line 5x-3y+6=0: a. -12/5 b.5/12 c.-12/5 d.2/5 e. none 48. The equation of a line which passes through the midpoint the line segment with end points (4,2) and (8,6) and perpendicular to the line given by 3x+4y-3=0 is: a. y + x=10 b.-4x+3y+12=0 c.4y-3x+3=0 d.3x-4y+12=0 e. none 49.The coordinates of the vertices of ABC are A(0,4) b(-2,-4) and C(4,-4) then the three medians of the triangle meet at: 50. The vertices of a PQR are P(-2, 3),Q(4,-2) and R(6,-1) then Find the length of the median from P. Find the length of the altitude from Q. 52. The vertices of a triangle are A(-2,4) B(6,10) C(4,6) Find: a. the equation of the median from C b. The equation of the altitude to BC c. The point of intersection of the three medians (centroid) : use any method!
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