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The diagram below shows the shape $g$ on a grid - Junior Cycle Mathematics - Question 3 - 2019
Question 3
The diagram below shows the shape $g$ on a grid. The points $P$ and $S$ are also marked. Each small square on the grid has sides of length 1 cm. (a) Find the length... show full transcript
Worked Solution & Example Answer:The diagram below shows the shape $g$ on a grid - Junior Cycle Mathematics - Question 3 - 2019
Step 1
Find the length of the perimeter of the shape g
Answer
To calculate the perimeter of shape , we will first identify all the sides of the shape. The lengths of the adjacent sides are as follows:
- Vertical side: 3 cm (from point down to the first horizontal line)
- Horizontal side: 1 cm (from the end of the vertical side to the next vertical line)
- Vertical side: 1 cm (going upwards to the next level)
- Horizontal side: 4 cm (from the end of the upward vertical to the endpoint of the shape)
- Vertical side: 3 cm (going down back to the base)
Now, we calculate the perimeter:
Step 2
Draw the image of the shape g under the translation that sends the point P to the point S
Answer
To find the image of shape under the specified translation, we first determine the translation vector. The point moves to point . We identify the translation:
- The coordinates of point are (1, 0)
- The coordinates of point are (1, 3)
- The translation vector is thus .
We apply this translation vector to all vertices of shape to obtain the new positions of each vertex and redraw the shape accordingly. The shape is then translated upwards by 3 units.