CAT Questions and answers on coordinate geometry:
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(Coordinate Geometry Important Questions PDF) Coordinate geometry is a branch of geometry where the location of the points on the plane is defined with the help of a methodical pair of numbers also known as coordinates. In this Blog, we have provided Coordinate Geometry Important Questions PDF. Coordinate geometry is where algebra lights geometry. Using coordinate geometry, trigonometry and radians, and complex numbers. Objectives: Students will use the coordinate plane and equations of lines and circles to describe figures. Create the equation of a circle given the figure or use the structure of a given equation to determine a property of a figure in the coordinate plane.
Question 1:
What is the reflection of the point (4 , -3) in the line y = 1?
a) (4, -5)
b) (4, 5)
c) (-4, -5)
d) (-4, 5)
b) (4, 5)
c) (-4, -5)
d) (-4, 5)
Question 2:
At what point does the line 3x + 2y = -12 intercept the Y-axis?
a) (0,6)
b) (0,-6)
c) (-4,0)
d) (4,0)
b) (0,-6)
c) (-4,0)
d) (4,0)
Question 3:
The area of triangle with vertices (5x,2x), (7x, 0) and (5x, 0) is 72 sq units. If x is a positive integer, what is the value of x?
a) 6
b) 3
c) 9
d) 12
e)15
b) 3
c) 9
d) 12
e)15
Question 4:
Find the intercepts made by the line 7x + 6y – 42 = 0 on y and x axis respectively.
a) (6,7)
b) (3,2)
c) (2,3)
d) (7,6)
b) (3,2)
c) (2,3)
d) (7,6)
Question 5:
If the coordinates of the point that is a reflection of (3,2) with respect to 2x+y=5 are (a,b), then find the value of (a+b-0.4).
Answer: 1
Solution:
Line perpendicular to 2x+y=5 has a slope of 1/2.
Line passing through (3,2) with a slope of 1/2 => y-2 = 1/2(x-3)
2y-4 = x-3 => x-2y = -1
Intersection point = (9/5,7/5)
Reflection point = (a,b)
(9/5, 7/5) is the midpoint of (3,2) and (a,b). Hence, by midpoint formula
(a+3)/2 = 9/5 => a = 3/5
(b+2)/2 = 7/5 => b = 4/5
a+b-0.4 = 1.4 – 0.4 = 1
(a+3)/2 = 9/5 => a = 3/5
(b+2)/2 = 7/5 => b = 4/5
a+b-0.4 = 1.4 – 0.4 = 1
Solutions (1 to 4)
1) Answer (b)
Reflection of point (x,y) in line y=a is (x,-y+2a)
Now, Reflection of point (4,-3) in line y=1
= [4,3+2(1)]=(4,5)
=> Ans – (B) Cs go apk download.
Now, Reflection of point (4,-3) in line y=1
= [4,3+2(1)]=(4,5)
=> Ans – (B) Cs go apk download.
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2) Answer (b)
The line 3x + 2y = -12 will intercept the y-axis at x = 0
Thus, substituting value of x in above equation
=> 3(0) + 2y = -12
=> y = -12/2 = -6
Thus, the line will intercept y axis at (0,-6)
=> Ans – (B)
Thus, substituting value of x in above equation
=> 3(0) + 2y = -12
=> y = -12/2 = -6
Thus, the line will intercept y axis at (0,-6)
=> Ans – (B)
3) Answer (a)
The diagram with the given vertices is given below:
ABC is a right angled triangle with AB = BC = 2x and right angles at $$angle ABC$$
Thus, area of the triangle = 1/2 * AB * BC = 1/2 * 2x * 2x = $$2x^2$$ = 72
=> x = $$pm$$6
Since x is positive, x = 6
Thus, area of the triangle = 1/2 * AB * BC = 1/2 * 2x * 2x = $$2x^2$$ = 72
=> x = $$pm$$6
Since x is positive, x = 6
Coordinate Geometry Practice Test Pdf
4) Answer (d)
Coordinate Geometry Exercises
The point where this line cuts the x axis, y coordinate will be 0 and the point where it cuts the y axis, x coordinate would be 0.
So y intercept = 7*0 + 6y = 42 => y = 7
Similarly x intercept = 7x + 6*0 = 42 => x = 6
Since the question asks the intercepts in the order y and x respectively, the correct answer is (7, 6)
Thus option D is the correct answer.
So y intercept = 7*0 + 6y = 42 => y = 7
Similarly x intercept = 7x + 6*0 = 42 => x = 6
Since the question asks the intercepts in the order y and x respectively, the correct answer is (7, 6)
Thus option D is the correct answer.