Coordinate Geometry
Math ⇒ Geometry
Coordinate Geometry starts at 8 and continues till grade 12.
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See sample questions for grade 12
Explain the meaning of the term 'locus' in coordinate geometry.
Find the area of the triangle with vertices at (0, 0), (4, 0), and (4, 3).
Find the equation of the circle passing through the origin and having center at (3, -2).
Find the equation of the line passing through (1, 2) and (3, 6).
Find the equation of the line that passes through the intersection of the lines x + y = 4 and x - y = 2 and is parallel to the x-axis.
Given the points A(1, 2), B(4, 6), and C(7, 2), determine if triangle ABC is isosceles.
If the points (x, 2), (3, 4), and (5, 6) are collinear, the value of x is __________.
The length of the median from vertex A of triangle ABC with vertices A(1, 2), B(4, 6), and C(7, 2) is __________.
Which of the following is the correct formula for the distance from point (x₁, y₁) to the line Ax + By + C = 0?
(1) |Ax₁ + By₁ + C| / √(A² + B²)
(2) |Ax₁ - By₁ + C| / √(A² + B²)
(3) |Ax₁ + By₁ - C| / √(A² + B²)
(4) |Ax₁ - By₁ - C| / √(A² + B²)
Which of the following is the equation of a circle with center at (2, -1) and radius 5?
(1) (x-2)² + (y+1)² = 25
(2) (x+2)² + (y-1)² = 25
(3) (x-2)² + (y-1)² = 25
(4) (x+2)² + (y+1)² = 25
Which of the following is the equation of a line passing through (0, 0) and parallel to the line 2x - 3y + 5 = 0?
(1) 2x - 3y = 0
(2) 3x + 2y = 0
(3) 2x + 3y = 0
(4) 3x - 2y = 0
Which of the following is the equation of a line with slope 3 and y-intercept -2?
(1) y = 3x - 2
(2) y = -2x + 3
(3) y = 3x + 2
(4) y = -3x - 2
If the points (x, 2), (3, 4), and (5, 6) are collinear, the value of x is __________.
The coordinates of the centroid of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) are __________.
The equation of a circle with center at the origin and passing through the point (a, b) is __________.
The equation of a line parallel to y = -3x + 2 and passing through (1, 4) is __________.
Given the points A(1, 2), B(4, 6), and C(7, 2), determine if triangle ABC is isosceles.
True or False: The area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is given by (1/2)|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|.
True or False: The locus of points equidistant from two fixed points is the perpendicular bisector of the segment joining them.
True or False: The slope of a line perpendicular to a line with slope m is -1/m.
