OKAY

Geometry Level 1

As illustrated in the above diagram, four points O = ( 1 , − 3 ) , K = ( a , b ) , A = ( c , d ) , Y = ( 2 , 7 ) O = (1,-3), K = (a,b), A=(c,d), Y= (2,7) lie on the same line segment. If O K = K A = A Y , OK=KA=AY, what is the value of a + b + c + d ? a+b+c+d?


The answer is 7.

View wiki
Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Using Section Formula .

In O A ‾ \overline{OA} .
⇒ 1 + c 2 = a \Rightarrow \dfrac{1+c}{2}=a ..... ( 1 ) (1)

⇒ − 3 + d 2 = b \Rightarrow \dfrac{-3+d}{2}=b ..... ( 2 ) (2)

Now, In K Y ‾ \overline{KY} .
⇒ a + 2 2 = c \Rightarrow \dfrac{a+2}{2}=c ..... ( 3 ) (3)

⇒ b + 7 2 = d \Rightarrow \dfrac{b+7}{2}=d ..... ( 4 ) (4) .

Adding ( 1 ) , ( 2 ) , ( 3 ) (1),(2),(3) and ( 4 ) (4) .
⇒ a + b + c + d = a + b + c + d + 7 2 \Rightarrow a+b+c+d=\dfrac{a+b+c+d+7}{2}
⇒ a + b + c + d = 7 . \Rightarrow a+b+c+d=\boxed{7}.

2 Helpful 1 Interesting 1 Brilliant 0 Confused

Used same approach .

Vignesh Rao - 5 years, 5 months ago

First you can find the coordinates of either K or A by dividing line segment in ratio 1:2 or 2:1 respectively. Then bisect the double length segment to get final coordinate pair.

1 Helpful 1 Interesting 1 Brilliant 1 Confused

very smart and tricky way enjoyed this method

amulya Peerla - 2 years, 7 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...