Problem 8 Easy Difficulty

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

Answer

Related Courses

Geometry

NCERT Class 10 - Math

Chapter 7

Coordinate Geometry

Section 4

Area of a Triangle

Discussion

You must be signed in to discuss.

Top Geometry Educators

Watch More Solved Questions in Chapter 7

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Video Transcript

So we have our number eight. The question says that abc is a B C D. Is a rectangle formed by The points -1, -1 come up for. And these are all the parts and people are as a P Q R. S at the midpoint. Okay, we have to just draw first. A B c D is a rectangle is minus one common minus one. B s minus one comma. For She is 5:04 and they is five on -1. And this is B midpoint pure are and as so people have coordinate minus one plus minus one minus two by two minus one comma. There is one thing three x 2. Q. with .5 Plus -1. So four by two and for are will be five plus 5, 10 by 25 and three x 2 as will pay two comma minus one. So these are the points. Okay, that's true. Let us find PQ PQ which will be two plus one whole square place four minus three by two whole square under the square root. So nine plus 25 x four, 61 161 x two. Now cuba will be five minus two. Hold square place three x 2 -4 Whole Square. So 161 x two. R. S. Will be called two to minus five or square place -1 -3 x two. World square. Which will be controlled Under 61 x two. and SB Will be 2-plus 1 whole square place minus one minus three x 2 Old Square. So this philosophy under 61 x two. Now the diagnosis. If he assumed so diagnosed we have just done like this will be now finding the diagonals. This ask you and be oh sp that the we have already found out the sp so be our first Darnell P. R. That would be five plus one whole square Plus three x 2 -3 x two. Old Square 36, which is six. And Us will be able to to -2 Old Square. Place three by I'm sorry, less four plus one whole square. This is fight. So we can see that we have been killed. Equal to you are equal to r is equal to sp but we are not equal to Q. S. O. P. Q R S is a rhombus.

Get More Help with this Textbook