Practice Questions for Geometry - Coordinate Geometry

1. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the distance between the points A (3, 5) & B (6, 1)

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Answer: 5

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Explanation :

Distance between two points (x₁, y₁) and (x₂, y₂) is $\sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

∴ Distance between A (3, 5) & B (6, 1) = $\sqrt{{(6 - 3)}^{2} + {(1 - 5)}^{2}}$ = $\sqrt{3^{3} + 4^{2}}$ = 5

Hence, 5.

2. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the equation of the line passing through A (4, -3) and parallel to the y-axis.

(a)
y = - 3
(b)
x = 4
(c)
y = 0
(d)
x = - 3

3. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the equation of the line passing through A (4, -3) and parallel to the x-axis.

(a)
y = -3
(b)
x = 4
(c)
y = 0
(d)
x = -3

4. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the value of ‘k’, if (3x + y - 4) - k(5x - 4y + 10) = 0 is parallel to x axis.

(a)
3/5
(b)
1/4
(c)
-1/4
(d)
None of these

5. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the center of the circle which has A (2, 9) & B (0, 11) as the extremities of its diameter.

(a)
(1, 10)
(b)
(2, 20)
(c)
(1, -1)
(d)
None of these

Answer: Option A

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Explanation :

Center of a circle is located in the middle of the diameter.

Hence, the center is $(\frac{2 + 0}{2}, \frac{9 + 11}{2})$ = (1, 10)

Hence, option (a).

6. CRE 1 - Basics | Geometry - Coordinate Geometry

Compute the slope of the line passing through the points A (4, 1) & B (6, 2)

(a)
2
(b)
1/2
(c)
-1/2
(d)
None of these

Answer: Option B

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Explanation :

Slope between two points (x₁, y₁) and (x₂, y₂) is given by $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

∴ Slope between the points A (4, 1) & B (6, 2) is $\frac{2 - 1}{6 - 4} = \frac{1}{2}$

Hence, option (b).

7. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the equation of the line which passes through (2, -2) and has a slope 2.

(a)
2x + y = 2
(b)
y - 2x = 6
(c)
2x - y = 6
(d)
None of these

Answer: Option C

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Explanation :

Equation of a line passing through (x₁, y₁) with slope m is $\frac{y - y_{1}}{x - x_{1}} = m$

∴ Equation of the required line is $\frac{y - (- 2)}{x - 2}$ = 2

⇒ 2x – 4 = y + 2

⇒ 2x – y = 6

Hence, option (c).

8. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the value of ‘k’ for which the three points A (-1, 10), B (k, 2) & C (17/5, 26/5) are collinear.

(a)
19/3
(b)
-19/3
(c)
6
(d)
None of these

Answer: Option A

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Explanation :

For 3 or more points to be collinear they should have the same slope.

∴ Slope of A and B should be same as slope of A and C.

⇒ $\frac{10 - 2}{- 1 - k} = \frac{10 - \frac{26}{5}}{- 1 - \frac{17}{5}}$

⇒ $- \frac{8}{k + 1} = - \frac{24}{22}$

⇒ k + 1 = 22/3

⇒ k = 19/3

Hence, option (a).

9. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the slope and the y-intercept of the line y = 3x - 15.

(a)
-3 and -15
(b)
3 and 15
(c)
3 and -15
(d)
None of these

Answer: Option A

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Explanation :

A line with x and y intercepts as a and b respectively is $\frac{x}{a} + \frac{y}{b}$ = 1.

∴ Required line is $\frac{x}{2} + \frac{y}{- 3}$ = 1

⇒ -3x + 2y = -6

⇒ 3x – 2y = 6

Hence, option (a).

10. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the x-intercept & y-intercept of the line 3x - 2y - 24 = 0.

(a)
8 and -12
(b)
8 and 12
(c)
-8 and -12
(d)
None of these

11. CRE 1 - Basics | Geometry - Coordinate Geometry

Write the intercept form of the line whose general form is 4x + 3y – 24 = 0.

(a)
$\frac{x}{8} + \frac{y}{6} = 1$
(b)
$\frac{x}{6} + \frac{y}{8} = 1$
(c)
$\frac{x}{8} - \frac{y}{6} = 1$
(d)
None of these

Answer: Option B

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Explanation :

Intercept form of a line is $\frac{x}{a} + \frac{y}{b} = 1$

Given line is 4x + 3y – 24 = 0.

⇒ 4x + 3y = 24

⇒ $\frac{x}{6} + \frac{y}{8} = 1$

Hence, option (b).

12. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the general form equation of the line joining the points A (3, 1) & B (0, -1).

(a)
2x – 3y + 3 = 0
(b)
2x + 3y – 3 = 0
(c)
2x – 3y – 3 = 0
(d)
None of these

Answer: Option C

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Explanation :

General equation of a line joining points (x₁, y₁) and (x₂, y₂) is $\frac{y - y_{2}}{x - x_{2}} = \frac{y_{1} - y_{2}}{x_{1} - x_{2}}$

∴ $\frac{y - (- 1)}{x - 0} = \frac{1 - (- 1)}{3 - 0}$

⇒ 3y + 3 = 2x

⇒ 2x – 3y – 3 = 0

Hence, option (c).

13. CRE 1 - Basics | Geometry - Coordinate Geometry

Which of the following best describes the relation between the lines 6x - 9y - 4 = 0 & -4x + 6y - 13 = 0?

(a)
Prallel
(b)
Intersection, not perpendicular
(c)
Perpendicular
(d)
None of these

14. CRE 1 - Basics | Geometry - Coordinate Geometry

Which of the following best describes the relation between the lines 6x + 10y - 19 = 0 & 5x - 3y + 17 = 0?

(a)
Parallel
(b)
Intersectiong, not perpendicular
(c)
Perpendicular
(d)
None of these

15. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the equation of line passing through (2,-3) and parallel to x + 3y + 12 = 0

(a)
3x - y + 7 = 0
(b)
x + 3y + 7 = 0
(c)
x + 3y - 7 = 0
(d)
None of these

16. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the equation of line passing through (2,-3) and perpendicular to x + 2y + 12 = 0.

(a)
2x - y – 7 = 0
(b)
x + 2y – 7 = 0
(c)
2x - y + 7 = 0
(d)
None of these

17. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the perpendicular distance of the point (1, 1) from the line 3x + 4y - 4 = 0.

(a)
4/5
(b)
2/5
(c)
3/5
(d)
None of these

Answer: Option C

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Explanation :

Distance of a point (x₁, y₁) from a line ax + by +c = 0 is $|\frac{a x_{1} + b y_{1} + c}{\sqrt{a^{2} + b^{2}}}|$

∴ The required distance = $\frac{3 \times 1 + 4 \times 1 - 4}{\sqrt{3^{2} + 4^{2}}}$ = 3/5

Hence, option (c).

18. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the co-ordinates of the point P which divides the line-segment joining the points A (7, 9) & B (8, 2) in the ratio 3 : 4 internally.

(a)
(7, 6)
(b)
(6, 6)
(c)
(52/7, 42/7)
(d)
None of these

Answer: Option C

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Explanation :

Coordinates of a point dividing (x₁, y₁) and (x₂, y₂) in the ratio a : b internally is given by $[\frac{b x_{1} + a x_{2}}{a + b}, \frac{b y_{1} + a y_{2}}{a + b}]$

∴ The coordinates of point P are $[\frac{4 \times 7 + 3 \times 8}{3 + 4}, \frac{4 \times 9 + 3 \times 2}{3 + 4}]$ = (52/7, 42/7)

Hence, option (c).

19. CRE 1 - Basics | Geometry - Coordinate Geometry

Find the co-ordinates of the point P which divides the line-segment joining the points A (2, -6) & B (3, 5) in the ratio 2:1 externally.

(a)
(8/3, 16/3)
(b)
(4, 6)
(c)
(4, 16)
(d)
None of these

Answer: Option A

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Explanation :

Coordinates of a point dividing (x₁, y₁) and (x₂, y₂) in the ratio a : b externally is given by $[\frac{b x_{1} - a x_{2}}{a - b}, \frac{b y_{1} - a y_{2}}{a - b}]$

∴ The coordinates of point P are $[\frac{2 \times 3 - 1 \times 2}{2 - 1}, \frac{2 \times 5 - 1 \times - 6}{2 - 1}]$ = (4, 16)

Hence, option (a).

CRE 1 - Basics | Geometry - Coordinate Geometry

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