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The scale drawing shows Katy's garden ABCD - OCR - GCSE Maths - Question 19 - 2018 - Paper 1
Question 19
The scale drawing shows Katy's garden ABCD. Scale: 1 cm represents 5 m. Katy places a statue in the garden. The statue is more than 30 m from D closer to CB than... show full transcript
Worked Solution & Example Answer:The scale drawing shows Katy's garden ABCD - OCR - GCSE Maths - Question 19 - 2018 - Paper 1
Step 1
more than 30 m from D
Answer
To find the region where the statue can be placed that is more than 30 m from point D, first calculate the distance in the drawing scale. Since 1 cm represents 5 m, 30 m will be represented as:
Now, draw a circle with a radius of 6 cm around point D. This circle represents all points that are exactly 30 m from D. Since the statue must be more than 30 m from D, the region outside this circle will be shaded.
Step 2
closer to CB than AB
Answer
To find the area where the statue is closer to line CB than line AB, we need to draw the angle bisector of angle ABC. This can be achieved by using a ruler to create a line that is equidistant from lines AB and CB, which will be situated at an angle to both lines. Mark this bisector and extend it appropriately within the garden area until it meets the boundary of the garden ABCD.
Next, all of the points to one side of this bisector will be the area where the statue can be located that is closer to line CB than line AB.
Step 3
Construct and shade the region
Answer
Now, combine the two regions found above. The shaded region where the statue can be placed will be the area outside the circle (more than 30 m from D) and on the side of the bisector of angle ABC that is closer to line CB than line AB. Shade this region carefully on your drawing, and ensure that all construction lines (the circle and the bisector) are clearly marked.