Solve all Q1, 2, 3 explaining detailly each step COORDINATE GEOMETRYa) MCQS:1. Q (a1, b¡) and R(a, b2) are two points on a line segment PR. If Q is the midpoint of PR thecoordinates of P are:A. (a – a3, 2b, – b;) B. (*a2 D: C. (2a1 – a3,A1+a2 b1+b2)C. (2a1 – az.2b1 - b2)D. (2a2 - a1, 2b - b1)|22. An equation of the line L,is 3x + 4y = 5. Another line L2 passes through the point (1,2) andis perpendicular to Lq. Find the equation of L2A. 3x – 4y = -2Find the coordinates of a point which divides the line segment joining the points (4,1) andB. 4x – 3y = -2C. 4x – 3y = 2D. 3x – 4y = 2%3D--(7.7) in the ratio 2:1A. (6.5)В. (5.5)C. (5,6)D. (6,3)4. The coordinates of the point which divides internally the line joining the points (2,4) and (-3, 9) in the ratio 1:4 are:A. (5, 1) B. (1, 5) C. ()D. ()-11-7-1133325. M and N are points with coordinates (2, 6) and (3, 5) respectively. The coordinates of thepoint which divides the line segment MN externally in ratio 2: 1 are:8 16A. (,)B. ()16 8D. ()6. The tangent of the acute angle between the lines 2x -y = 1 and 4x + 3y = 2 is:5 11)C. (4, 4)133 3.2%3DA. 2 B.-3 C.() D. )10Á. 211/.5.7. Find the equation of a line through the origin which is inclined at - to the line:2x + 3y-4 = 0A. x - y= 0 B. x – 5y 0 C. 3y +5x = 0 D. 2x + y= 08. The curve y = ax- x cuts the line y = 3x at right angles. The possible values of a are:IT4%3D1 19A. 4,-3 B. 3, - 3 C.-, 19 D.ww.3' 39. The least distance from the origin to the curve y rx + 5 occurs when x 2. The value ofthe constant r is:B. -10. To reduce y = ax" to a linear form a straight line is obtained by plotting:5A. --4C. 2D. 42A. x against y B. x against log y C. log x against logy D. - against -y11.The gradient of the straight line obtained when: "+-a1 is reduced to a linear form is:y1A. – 212. The relation y = a*Dis reduced to form Y = mx + c. the values of m and c are given by:1В. -C.-b.D.-aaaax+b:A. m = a, c = b B. m Ina, c= InbC. m13. M (1, -2) and N (6, 8) are two points in the X - y plane. The equation of the locus of theb,c = blna D. m Ina, c = blnaapoint P which moves in such a way that MP:NP = 3:2 is:A. x+y + 2x+ 16y- 5 0C. 3x² + 3:-- x+ 24y – 5 = 0 D. 3x + 3y“ – 20x – 36y + 95 = 0B. x + y - 10x -- 20y + 45 = 064

Answered: Image /qna-images/answer/c1d7b5de-003e-41d1-b716-f0d5a626817e.jpg

COORDINATE GEOMETRY a) MCQS: 1. Q (a1, b;) and R(a, b2) are two points on a line segment PR. If Q is the midpoint of PR the coordinates of P are: A. (a - az, 2b, - b;) B. a1+a2 b+b2 2)C. (2a1 - a. 2b, - b) D. (2a, - aj, 2b - b1) 2. An equation of the line L, is 3x + 4y = 5. Another line L2 passes through the point (1,2) and is perpendicular to L,. Find the equation of L2 A. 3x – 4y = -2 3. Find the coordinates of a point which divides the line segment joining the points (4,1) and B. 4x – 3y = -2 C. 4x – 3y = 2 D. 3x - 4y = (7.7) in the ratio 2:1 A. (6.5) B. (5.5) C. (5.6) D. (6,3)

COORDINATE GEOMETRY a) MCQS: 1. Q (a1, b;) and R(a, b2) are two points on a line segment PR. If Q is the midpoint of PR the coordinates of P are: A. (a - az, 2b, - b;) B. a1+a2 b+b2 2)C. (2a1 - a. 2b, - b) D. (2a, - aj, 2b - b1) 2. An equation of the line L, is 3x + 4y = 5. Another line L2 passes through the point (1,2) and is perpendicular to L,. Find the equation of L2 A. 3x – 4y = -2 3. Find the coordinates of a point which divides the line segment joining the points (4,1) and B. 4x – 3y = -2 C. 4x – 3y = 2 D. 3x - 4y = (7.7) in the ratio 2:1 A. (6.5) B. (5.5) C. (5.6) D. (6,3)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

Solve all Q1, 2, 3 explaining detailly each step

COORDINATE GEOMETRY
a) MCQS:
1. Q (a1, b¡) and R(a, b2) are two points on a line segment PR. If Q is the midpoint of PR the
coordinates of P are:
A. (a – a3, 2b, – b;) B. (*a2 D: C. (2a1 – a3,
A1+a2 b1+b2
)C. (2a1 – az.
2b1 - b2)
D. (2a2 - a1, 2b - b1)
|
2
2. An equation of the line L,is 3x + 4y = 5. Another line L2 passes through the point (1,2) and
is perpendicular to Lq. Find the equation of L2
A. 3x – 4y = -2
Find the coordinates of a point which divides the line segment joining the points (4,1) and
B. 4x – 3y = -2
C. 4x – 3y = 2
D. 3x – 4y = 2
%3D
--
(7.7) in the ratio 2:1
A. (6.5)
В. (5.5)
C. (5,6)
D. (6,3)
4. The coordinates of the point which divides internally the line joining the points (2,4) and (-
3, 9) in the ratio 1:4 are:
A. (5, 1) B. (1, 5) C. ()
D. ()
-11
-7
-1
13
3
3
2
5. M and N are points with coordinates (2, 6) and (3, 5) respectively. The coordinates of the
point which divides the line segment MN externally in ratio 2: 1 are:
8 16
A. (,)
B. ()
16 8
D. ()
6. The tangent of the acute angle between the lines 2x -y = 1 and 4x + 3y = 2 is:
5 11)
C. (4, 4)
13
3 3.
2
%3D
A. 2 B.-3 C.() D. )
10
Á. 2
11/
.5.
7. Find the equation of a line through the origin which is inclined at - to the line:2x + 3y-4 = 0
A. x - y= 0 B. x – 5y 0 C. 3y +5x = 0 D. 2x + y= 0
8. The curve y = ax- x cuts the line y = 3x at right angles. The possible values of a are:
IT
4
%3D
1 19
A. 4,-3 B. 3, - 3 C.
-, 19 D.
ww.
3' 3
9. The least distance from the origin to the curve y rx + 5 occurs when x 2. The value of
the constant r is:
B. -
10. To reduce y = ax" to a linear form a straight line is obtained by plotting:
5
A. --4
C. 2
D. 4
2
A. x against y B. x against log y C. log x against logy D. - against -
y
11.The gradient of the straight line obtained when: "+-
a
1 is reduced to a linear form is:
y
1
A. – 2
12. The relation y = a*Dis reduced to form Y = mx + c. the values of m and c are given by:
1
В. -
C.-
b.
D.
-
a
a
a
a
x+b:
A. m = a, c = b B. m Ina, c= InbC. m
13. M (1, -2) and N (6, 8) are two points in the X - y plane. The equation of the locus of the
b
,c = blna D. m Ina, c = blna
a
point P which moves in such a way that MP:NP = 3:2 is:
A. x+y + 2x+ 16y- 5 0
C. 3x² + 3:-- x+ 24y – 5 = 0 D. 3x + 3y“ – 20x – 36y + 95 = 0
B. x + y - 10x -- 20y + 45 = 0
64

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