## CAT Questions and answers on coordinate geometry:

CAT Questions on co-ordinate geometry PDF

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**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)

**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)

**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

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**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)

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**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

**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)

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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)

**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

**4) Answer (d)**

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.

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