Coordinate Geometry Questions and Answers

Q: Which of the following will be a point on a line that contains (−1, −1) and (2, 5)?

The point on the line is (100, 201).Find the equation of the line through (−1, −1) and (2, 5).\[ \begin{aligned} m &= \frac{5 - (-1)}{2 - (-1)} = \frac{6}{3} = 2 \\ y - 5 &= 2(x - 2) \\ y &= 2x + 1 \end{aligned} \]For \(x = 100\), \(y = 2(100) + 1 = 201\), so (100, 201) lies on the line.The other points fail the test: for \(x = 30\) the line gives 61, not 41; for \(x = 80\) it gives 161, not 91; and for \(x = 110\) it gives 221, not 121. Those options add 11 to \(x\), a pattern the two given points do not follow.

Q: What are the coordinates of the midpoint of the line segment joining the points (1, 5) and (7, 3)?

The midpoint averages the coordinates.\[ \left(\frac{1+7}{2},\ \frac{5+3}{2}\right) = (4,\ 4) \]

Q: What is the equation of a line with a slope of 3 and a y-intercept of 5?

The slope-intercept form is \( y = mx + c \).\[ y = 3x + 5 \]The slope multiplies \( x \) and the intercept stands alone - swapping them gives the first option.

Q: The point (0, -4) lies on:

A point with \( x = 0 \) lies on the y-axis, whatever its \( y \)-coordinate.The origin is the single point \( (0,0) \), and the first quadrant needs both coordinates positive.

Important Instructions

11.

Which of the following will be a point on a line that contains (−1, −1) and (2, 5)?

A.(30, 41)
B.(80, 91)
C.(100, 201)
D.(110, 121)

Exam Year(s)

Kerala PSC KAS - 2020,

Answer: C

The point on the line is (100, 201).

Find the equation of the line through (−1, −1) and (2, 5).

\[ \begin{aligned} m &= \frac{5 - (-1)}{2 - (-1)} = \frac{6}{3} = 2 \\ y - 5 &= 2(x - 2) \\ y &= 2x + 1 \end{aligned} \]

For \(x = 100\), \(y = 2(100) + 1 = 201\), so (100, 201) lies on the line.

The other points fail the test: for \(x = 30\) the line gives 61, not 41; for \(x = 80\) it gives 161, not 91; and for \(x = 110\) it gives 221, not 121. Those options add 11 to \(x\), a pattern the two given points do not follow.

Discuss in Forum

12.

In which quadrant does the point (-3, 5) lie?

A.First quadrant (i)
B.Second quadrant (ii)
C.Third quadrant (iii)
D.Fourth quadrant (iv)

Answer: B

The Cartesian coordinate system is divided into four quadrants.

Quadrant I: (+x, +y)
Quadrant II: (-x, +y)
Quadrant III: (-x, -y)
Quadrant IV: (+x, -y)

Since the point has a negative x-coordinate (-3) and a positive y-coordinate (5), it lies in the Second Quadrant.

Discuss in Forum

13.

What is the distance between the points (3, 2) and (6, 6)?

Answer: C

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\).

Distance = \(\sqrt{(6-3)^2 + (6-2)^2}\)

= \(\sqrt{3^2 + 4^2}\)

= \(\sqrt{9 + 16}\)

= \(\sqrt{25} = 5\) units.

Discuss in Forum

14.

What are the coordinates of the midpoint of the line segment joining the points (1, 5) and (7, 3)?

A.(3, 4)
B.(4, 4)
C.(8, 8)
D.(5, 4)

Answer: B

The midpoint averages the coordinates.

\[ \left(\frac{1+7}{2},\ \frac{5+3}{2}\right) = (4,\ 4) \]

Discuss in Forum

15.

What is the slope of the line passing through the points (2, 3) and (4, 7)?

A.1
B.2
C.3
D.1/2

Answer: B

\[ m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{7-3}{4-2} = 2 \]

Discuss in Forum

16.

What is the equation of a line with a slope of 3 and a y-intercept of 5?

A.Y = 5x + 3
B.Y = 3x + 5
C.X = 3y + 5
D.X = 5y + 3

Answer: B

The slope-intercept form is \( y = mx + c \).

\[ y = 3x + 5 \]

The slope multiplies \( x \) and the intercept stands alone - swapping them gives the first option.

Discuss in Forum

17.

The point (0, -4) lies on:

A.The x-axis
B.The y-axis
C.The origin
D.The first quadrant

Answer: B

A point with \( x = 0 \) lies on the y-axis, whatever its \( y \)-coordinate.

The origin is the single point \( (0,0) \), and the first quadrant needs both coordinates positive.

Discuss in Forum

18.

Find the coordinates of the point which divides the line segment joining (-1, 7) and (4, -3) in the ratio 2:3.

A.(1, 3)
B.(2, 1)
C.(3, 1)
D.(1, 1)

Answer: A

Using the section formula, the coordinates (x, y) are given by:

x = \(\frac{m_1x_2 + m_2x_1}{m_1+m_2}\) and y = \(\frac{m_1y_2 + m_2y_1}{m_1+m_2}\)

Here, \((x_1, y_1) = (-1, 7)\), \((x_2, y_2) = (4, -3)\), and \(m_1:m_2 = 2:3\).

x = \(\frac{2(4) + 3(-1)}{2+3} = \frac{8-3}{5} = \frac{5}{5} = 1\)

y = \(\frac{2(-3) + 3(7)}{2+3} = \frac{-6+21}{5} = \frac{15}{5} = 3\)

The coordinates are (1, 3).

Discuss in Forum

19.

What is the area of the triangle with vertices (1, -1), (-4, 6) and (-3, -5)?

A.21 sq units
B.24 sq units
C.25 sq units
D.28 sq units

Answer: B

The area of a triangle with vertices \((x_1, y_1), (x_2, y_2), (x_3, y_3)\) is given by the formula:

Area = \(\frac{1}{2} |x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)|\)

Area = \(\frac{1}{2} |1(6 - (-5)) + (-4)(-5 - (-1)) + (-3)(-1 - 6)|\)

Area = \(\frac{1}{2} |1(11) + (-4)(-4) + (-3)(-7)|\)

Area = \(\frac{1}{2} |11 + 16 + 21| = \frac{1}{2} |48| = 24\) sq units.

Discuss in Forum

20.

What is the slope of a line that is perpendicular to the line y = -3x + 4?

A.-3
B.3
C.1/3
D.-1/3

Answer: C

The given line is in the form y = mx + c, so its slope (m₁) is -3.

If two lines are perpendicular, the product of their slopes is -1. Let the slope of the perpendicular line be m₂.

m₁ × m₂ = -1

-3 × m₂ = -1

m₂ = \(\frac{-1}{-3} = \frac{1}{3}\).

Discuss in Forum

Coordinate Geometry Questions and Answers

Important Instructions

Topics

Other Subjects

Tags: Coordinate Geometry Questions and Answers || Coordinate Geometry MCQ || Geometry and Coordinates GK || Distance Formula Quantitative Aptitude || Coordinate Geometry MCQs

About Us

Coordinate Geometry Questions and Answers

Important Instructions

Topics

Other Subjects

Tags: Coordinate Geometry Questions and Answers || Coordinate Geometry MCQ || Geometry and Coordinates GK || Distance Formula Quantitative Aptitude || Coordinate Geometry MCQs

About Us

Stay informed about all important Dates & Notifications