Coordinate Geometry Exercises

A point that divides a line segment into two parts with a specific ratio

A line segment is divided into two parts by a point, AP = PQ = QB and the ratio is 1:2

A line segment is divided into two parts by a point, AP = PQ = QB, and the ratio is 2:1

A formula that determines the coordinates of the point that divides a line segment in a given ratio.

The distance between two points on a coordinate plane can be calculated using this formula.

A point that divides a line segment into two equal parts

The coordinate (2, 25) is the location of the green flag, since Niharika ran 1/4th the distance AD.

The coordinate (8, 20) is the location of the red flag, since Preet ran 1/5th the distance AD.

The point where a line intersects the x-axis is called the x-intercept. The y-coordinate of any point on the x-axis is always 0.

A parallelogram is a quadrilateral with opposite sides parallel and equal in length. The diagonals of a parallelogram bisect each other. This means they intersect each other at their midpoints.

The diameter of a circle is a line segment that passes through the center of the circle and has endpoints on the circle. The center of the circle is the midpoint of the diameter.

The ratio in which a line segment is divided by a point can be used to find the coordinates of the point of division. The coordinates of the point of division are a weighted average of the coordinates of the endpoints of the line segment, where the weights are given by the ratio.

The relationship between the lengths of line segments AP and AB can be represented by a ratio. If the ratio is known, the coordinates of point P can be calculated using the section formula.

The section formula is used to find the coordinates of a point that divides a line segment in a given ratio. The formula involves the coordinates of the endpoints of the line segment and the ratio in which the line segment is divided.

The area of a triangle is calculated by taking half the product of the base and its corresponding height.

A point that lies exactly in the middle of a line segment, dividing it into two equal parts.

The area of a quadrilateral can be calculated by dividing it into triangles and summing their individual areas.

The area of a triangle can be calculated using a formula involving the coordinates of its vertices.

The area of a triangle formed by joining the midpoints of the sides of a larger triangle is always one-fourth the area of the bigger triangle.

The midpoint formula is a special case of the section formula where the ratio is 1:1. It's used to find the midpoint of a line segment.

Two points on a coordinate plane are collinear when the points lie on the same line.

If three points are collinear, then the area of the triangle formed by them is zero. This is because a triangle doesn't exist if all points are on the same line.

The center of a circle is equidistant from all points on the circle's circumference. To find the center of a circle, calculate the midpoint of the line segment between any two points on the circle. This will give you the center.

The center of a circle is the point equidistant from all points on the circle. To find the center, use the fact that radii of the same circle are equal.

A square has four equal sides and four right angles. The diagonals of a square bisect each other at right angles, meaning they cut each other in half at their midpoints.

The coordinates of the center of a square can be found by averaging the x-coordinates and y-coordinates of two opposite vertices.

To find the coordinates of the other vertices of a square, use the fact that the sides are equal in length and the angles are right angles. You can use the distance formula to find the length of a side.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It can be used to find the length of a side of a right triangle if the lengths of the other two sides are known.

In a triangle, the line segment joining a vertex to the midpoint of the opposite side is called a median.

The point where all three medians of a triangle intersect is called the centroid.

The centroid divides each median in the ratio 2:1.

The coordinates of the centroid of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) are [(x1 + x2 + x3)/3, (y1 + y2 + y3)/3].

The area of a triangle can be calculated using the formula: Area = ½ × [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)], where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the triangle's vertices.

The coordinates of a point dividing a line segment internally in the ratio m1:m2 can be calculated using the formula: x = (m1x2 + m2x1)/(m1 + m2) and y = (m1y2 + m2y1)/(m1 + m2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints.