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CHEM PHYSICAL C

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Mathematics

Date

Nov 3, 2023

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2

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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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