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The quadrilateral ABCD is shown in the co-ordinate diagram below - Junior Cycle Mathematics - Question 11 - 2021
Question 11
The quadrilateral ABCD is shown in the co-ordinate diagram below. (a) Complete the table below to show the co-ordinates of the four corners of ABCD. Point A ... show full transcript
Worked Solution & Example Answer:The quadrilateral ABCD is shown in the co-ordinate diagram below - Junior Cycle Mathematics - Question 11 - 2021
Step 1
Step 2
On the diagram above, draw the image of ABCD under axial symmetry in the x-axis.
Answer
To draw the image of ABCD under axial symmetry in the x-axis, reflect each point over the x-axis:
- A (2, 4) becomes A' (2, -4)
- B (2, 0) becomes B' (2, 0)
- C (8, 0) becomes C' (8, 0)
- D (8, 4) becomes D' (8, -4)
Plot these points on the diagram.
Step 3
Work out the area of the shape ABCD.
Answer
To find the area of quadrilateral ABCD, it can be divided into a rectangle and a triangle.
-
Rectangle ABCD:
- Length = |x_D - x_A| = |8 - 2| = 6
- Height = |y_A - y_B| = |4 - 0| = 4
- Area = Length × Height = 6 × 4 = 24
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The area of the rectangle ABCD is:
- Area = 24 square units.
Step 4
Write each line segment from the list above into the correct place in the table below, to match each line segment to its equation.
Answer
The equations corresponding to each line segment are as follows:
- [AB]: y = 4 (horizontal line at y = 4)
- [BC]: y = 0 (horizontal line at y = 0)
- [CD]: y = x - 7 (diagonal line segment)
- [AD]: x = 8 (vertical line at x = 8)