## Show that the points a(2 2) b(5 7) c(–5 13) and d(–8 8) are the vertices of a rectangle.

Contents

- Show that the points a(2 2) b(5 7) c(–5 13) and d(–8 8) are the vertices of a rectangle.
- If `a(-3,5),b(-2,-7),c(1,-8)a n dd(6,3)` are the vertices of a
- Find fourth vertex of rectangle coordinate geometry
- Show that the points a(3, 0), b(6, 4) and c(-1, 3
- Prove that the diagonals of a rectangle abcd with vertices a(2

## If `a(-3,5),b(-2,-7),c(1,-8)a n dd(6,3)` are the vertices of a

The location of a point in relation to the origin is defined by an ordered pair (x, y). If the x-coordinate is positive, it represents a position to the right of the origin; if it is negative, it represents a position to the left of the origin. If the y-coordinate is positive, it represents a position above the origin; if it is negative, it represents a position below the origin. Each location (point) in the plane is uniquely defined using this method. For instance, as shown, the pair (2, 3) denotes the location relative to the origin:

The Cartesian coordinate system is the name given to this system.

When referring to the rectangular coordinate system, this term is named after René Descartes (1596–1650), a French mathematician.

The plane is divided into four quadrants by the x- and y-axes.

The four regions of a rectangular coordinate plane partly bounded by the x- and y-axes and numbered I, II, III, and IV, as shown, are called with roman numerals I, II, III, and IV. Both coordinates in quadrant I are positive. The x-coordinate in quadrant II is negative, while the y-coordinate is positive. Both coordinates in quadrant III are negative. The x-coordinate in quadrant IV is positive, while the y-coordinate is negative.

## Find fourth vertex of rectangle coordinate geometry

Q.5. Four friends are seated in a classroom at points A, B, C, and D, as shown in Fig. Champa and Chaneli enter the classroom, and after a few moments of observation, Champa asks Chaneli, “Don’t you think ABCD is a squar?” Chaneli isn’t so confident. Determine which of them is right using the distance single formula.

Q.3. In your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each to perform Sports Day activities. As shown in the diagram, 100 flower pots were positioned at a distance of 1 m apart along AD. On the second line, Niharika runs the distance AD and posts a green flag. Preet posts a red flag after running the distance AD on the eighth line. What is the difference in size between the two flags? Where does Rashmi place her blue flag if she has to place it exactly halfway between the two flags’ line segments?

Q.3. Measure the area of the triangular created by joining the midpoints of the sides of the triangle whose vertices are (0, –1), (2, 1), and (3, 1), respectively (0, 3). Calculate the area of this triangle in relation to the area of the given triangle.

### Show that the points a(3, 0), b(6, 4) and c(-1, 3

This will help students clear up any questions they may have and develop their application skills as they prepare for board exams. The thorough, step-by-step solutions will assist you in better understanding the concepts and resolving any confusions you might have.

Section Formula, Graphs of Linear Equations, Distance Formula, Coordinate Geometry, Coordinate Geometry, Basic Geometric Constructions, Area of a Triangle, Section Formula, Graphs of Linear Equations, Distance Formula, Coordinate Geometry, Coordinate Geometry, Basic Geometric Constructions, Area of a Triangle, Section Formula, Graphs of Linear Equations, Distance Formula, Coordinate Geometry, Coordinate Geometry, Coordinate Geometry, Basic Geometric Constructions, Area of

RS Aggarwal Class 10 solutions are used. Students can easily prepare for exams by doing Coordinate Geometry exercises, which include solutions structured chapter-by-chapter and page-by-page. The questions answered in RS Aggarwal Solutions are crucial.

### Prove that the diagonals of a rectangle abcd with vertices a(2

The mid-point of (EG) is equal to the mid-point of (EG) since the diagonal bisects each other (FH\). Since we have the co-ordinates of both (E) and (G), we can first measure the mid-point of (EG) (G\). We can then use the midpoint to assist us in locating the coordinates of (H\).

To see if opposite sides are parallel, we must determine the gradients of each side. We’ve already measured the gradient of (PS), so all we have to do now is verify the gradients of the remaining three sides. However, (PS) is not parallel to (QR) in our sketch (you can verify this by measuring the gradient of (QR)).

(m PQ times m QR), (m QR times m PR), and (m PQ times m PR) are now available to search. We have shown that the triangle is right-angled when one of these values equals (-text1).

Finally, we measure the lengths of the triangle’s sides (PQ) and (RQ) to prove that it is isosceles. We don’t need to measure (PR) since it is the triangle’s hypotenuse and must be longer than (PQ) and (PQ) (RQ\).