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The diagram below shows the shape $g$ on a grid - Junior Cycle Mathematics - Question 3 - 2019

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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.

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Answer

To find the perimeter of shape gg, we need to add the lengths of all its sides. Observing the shape:

  1. The bottom side is 5 units long.
  2. The left vertical side is 4 units long.
  3. The top horizontal side is 3 units long.
  4. The right vertical side descends 2 units, followed by an additional 2 units (totaling 4 units).

Calculating the perimeter:

extPerimeter=5+4+3+4=16 cm ext{Perimeter} = 5 + 4 + 3 + 4 = 16 \text{ cm}

Step 2

Draw the image of the shape g under the translation that sends the point P to the point S.

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Answer

To draw the shape gg under the translation that sends point PP to point SS, we first determine the translation vector. The coordinates of points PP and SS need to be identified. If point PP is at (x1,y1)(x_1, y_1) and point SS is at (x2,y2)(x_2, y_2):

  • The translation vector can be calculated as:

extTranslationVector=(x2−x1,y2−y1) ext{Translation Vector} = (x_2 - x_1, y_2 - y_1)

This vector is then applied to each vertex of shape gg to find their new positions. After applying the translation, the shape should be redrawn accordingly, ensuring that all corresponding vertices of the original shape retain their relative positions.

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