26 X, Y, and Z are three points on a horizontal sea level map as shown below. X is due North of Y and Z is due east of Y. Ship A is on a bearing of $070^\circ$ from X and on a bearing of $350^\circ$ from Z. It is given that 1 cm represents 2 km on the sea level.

(a)
Label the position of Ship A and write down the actual distance AX.

Answer AX = ... km
(b)
A boat, B stationed along path XZ is equidistant from Y and Z. Label the position of B.
(c)
Showing your constructions clearly, draw a circle with centre O, on the map such that the lines XY, YZ and XZ are tangents to the circle. Hence write down the radius of the circle on the map.

Answer ... cm

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Worked solution

26(b)

1. Construct the locus of points equidistant from $Y$ and $Z$.

With centres $Y$ and $Z$ and equal compass radius greater than half of $YZ$ , draw arcs above and below $YZ$ . Join the two arc intersections to form the perpendicular bisector of $YZ$ .

2. Locate $B$ on the given path $XZ$.

Mark the intersection of the perpendicular bisector of $YZ$ with the line segment $XZ$ and label it $B$ . Then $BY = BZ$ , and $B$ lies on $XZ$ .

Answer

Label $B$ at the point where the perpendicular bisector of $YZ$ meets $XZ$ .

AI analysis — may contain mistakes.

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26 X, Y, and Z are three points on a horizontal sea level map as shown below. X is due North of Y and Z is due east of Y. Ship A is on a bearing of 070∘070^\circ070∘ from X and on a bearing of 350∘350^\circ350∘ from Z. It is given that 1 cm represents 2 km on the sea level.

Worked solution

26(b)

More questions on this topic

26 X, Y, and Z are three points on a horizontal sea level map as shown below. X is due North of Y and Z is due east of Y. Ship A is on a bearing of $070^\circ$ from X and on a bearing of $350^\circ$ from Z. It is given that 1 cm represents 2 km on the sea level.