Point H is 6 m towards the East of point G, point R is 8 m North of point G. Point Q is exactly midway between Point R and point G. Point K is 10 m to the South of point Q. Point L is 3 m towards the East of point Q, point S is exactly midway between point G and point H.
(A) Point R is North-east of Point H.
(B) The shortest distance between Point H and Point R is 10 m
(C) The shortest distance between Point Q and Point S is 5 m.
(D) Point R is 14 m south of point K.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (B) and (C) only
Placing G at the start and marking every point by its distance east and north of G fixes the whole figure:
H is 6 m east of G, and S, midway between G and H, is 3 m east of G
R is 8 m north of G, and Q, midway between R and G, is 4 m north of G
K is 10 m south of Q, that is, \(10-4=6\) m south of G; L is 3 m east of Q
(A) Point R is North-east of Point H. Incorrect. R is 8 m north of G and H is 6 m east of G, so R lies to the north and to the west of H: R is north-west of H.
(B) The shortest distance between Point H and Point R is 10 m Correct. GH and GR meet at a right angle at G, so HR is the hypotenuse:
\(HR=\sqrt{6^{2}+8^{2}}=\sqrt{100}=10\) m
(C) The shortest distance between Point Q and Point S is 5 m. Correct. GQ = 4 m and GS = 3 m meet at a right angle at G:
\(QS=\sqrt{4^{2}+3^{2}}=\sqrt{25}=5\) m
(D) Point R is 14 m south of point K. Incorrect. R is 8 m north of G and K is 6 m south of G, so R is 14 m north of K, not south.