Question

Let `square`PQRS be a quadrilateral. If M and N are midpoints of the sides PQ and RS respectively then `bar"PS" + bar"OR"` = ______.

पर्याय

• `3bar"MN"`

• `4bar"MN"`

• `2bar"MN"`

• `2bar"NM"`

Answer 1

Let `square`PQRS be a quadrilateral. If M and N are midpoints of the sides PQ and RS respectively then `bar"PS" + bar"OR"` = `2bar"MN"`.

Explanation:

M and N are the midpoints of sides PQ and RS

∴ `bar"m" = (bar"p" + bar"q")/` and `bar"n" = (bar"r" + bar"s")/2`

⇒ `2bar"m" = bar"p" + bar"q"` and `bar"n" = bar"r" + bar"s"`

`bar"PS" + bar"QR" = bar"s" - bar"p" + bar"r" - bar"q"`

= `bar"r" + bar"s" - (bar"p" + bar"q")`

 `2bar"n" - 2bar"m"`

= `2bar"MN"`