Home
Class 10
MATHS
ABCD is a rectangle formed by the points...

ABCD is a rectangle formed by the points `A(1,\ 1),``B(1,\ 4),`` C(5,\ 4)` and `D(5,\ 1)`. P, Q, R and S are the midpoints of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? A rectangle? or a rhombus? Justify your answer.

Text Solution

AI Generated Solution

To determine whether the quadrilateral PQRS is a square, rectangle, or rhombus, we will follow these steps: ### Step 1: Find the midpoints P, Q, R, and S 1. **Midpoint P (of AB)**: - A(1, 1) and B(1, 4) - \( P = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{1 + 1}{2}, \frac{1 + 4}{2} \right) = \left( 1, \frac{5}{2} \right) \) ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|15 Videos

  • COORDINATE GEOMETRY

    NCERT ENGLISH|Exercise Exercise 7.1|10 Videos

  • COORDINATE GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 7.3|5 Videos

  • CONSTRUCTIONS

    NCERT ENGLISH|Exercise EXERCISE 11.2|7 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NCERT ENGLISH|Exercise EXERCISE 8.3|7 Videos

Similar Questions

Explore conceptually related problems

A B C D is a rectangle formed by joining the points A(-1,\ -1),\ \ B(-1,\ 4),\ \ C(5,\ 4) and D(5,\ -1)dot P ,\ Q ,\ R and S are the mid-points of sides A B ,\ B C ,\ C D and D A respectively. Is the quadrilateral P Q R S a square? a rectangle? or a rhombus? Justify your answer.

ABCD is a rhombus and P, Q, R and S are wthe mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

ABCD is a rhombus and P ,Q ,R ,S are the mid-points of A B ,B C ,C D ,D A respectively. Prove that P Q R S is a rectangle.

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

P,Q,R and S are the mid points of sides AB,BC , CD and DA respectively of rhombus ABCD. Show that PQRS is a rectangle. Under what conditions will PQRS be a square ?

ABCD is a square. P, Q and Rare the points on AB, BC and CD respectively, such that AP = BQ = CR. Prove that: PQ = QR

P, Q , R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD. Prove that PQRS is a rhombus.

ABCD is a square. P, Q and Rare the points on AB, BC and CD respectively, such that AP = BQ = CR. Prove that: PB = QC

If A, B, C are the points (-1, 5), (3, 1), (5, 7) respectively and D, E, F are the middle points of BC, CA and AB respectively, prove that Area of DeltaABC=4 DeltaDEF .

Home
Profile