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प्रश्न
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)
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उत्तर
Let the points (4, 5), (7, 6), (4, 3), and (1, 2) be representing the vertices A, B, C, and D of the given quadrilateral respectively.
∴ AB = `sqrt((4-7)^2+(5-6)^2)`
= `sqrt((-3)^2+(-1)^2)`
= `sqrt(9+1)`
= `sqrt10`
BC = `sqrt((7-4)^2+(6-3)^2)`
= `sqrt((3)^2+(3)^2)`
= `sqrt(9+9)`
= `sqrt18`
CD = `sqrt((4-1)^2+(3-2)^2)`
= `sqrt((3)^2+(1)^2)`
= `sqrt(9+1)`
= `sqrt10`
AD = `sqrt((4-1)^2+(5-2)^2)`
= `sqrt((3)^2+(3)^2)`
= `sqrt(9+9)`
= `sqrt18`
Diagonal AC = `sqrt((4-4)^2+(5-3)^2)`
= `sqrt((0)^2+(2)^2)`
= `sqrt(0+4)`
= 2
Diagonal CD = `sqrt((7-1)^2 + (6-2)^2)`
= `sqrt((6)^2+(4)^2)`
= `sqrt(36+16)`
= `sqrt52`
= `13sqrt2`
It can be observed that opposite sides of this quadrilateral are of the same length. However, the diagonals are of different lengths. Therefore, the given points are the vertices of a parallelogram.
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Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle: One such campaign board made by class X student of the school is shown in the figure.
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