The diagram below shows part of the frame of a swing on a co-ordinate grid - Junior Cycle Mathematics - Question 6 - 2014
Question 6
The diagram below shows part of the frame of a swing on a co-ordinate grid. Each unit on the grid represents one metre. The line segments [AB] and [AC] represent met... show full transcript
Worked Solution & Example Answer:The diagram below shows part of the frame of a swing on a co-ordinate grid - Junior Cycle Mathematics - Question 6 - 2014
Step 1
Write the co-ordinates of the points A, B and C in the spaces provided in the diagram.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The coordinates for the points are:
A: (0, 5)
B: (-4, 0)
C: (4, 0)
Step 2
Find the total length of metal bar needed to make this part of the swing.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The length of |AB| is calculated as:
|AC| = \\sqrt{(0 - 4)^2 + (5 - 0)^2} = \\sqrt{(-4)^2 + 5^2} = \\sqrt{16 + 25} = \\sqrt{41}$$
The total length of metal bar needed is:
$$2 imes |AB| = 2 imes \\sqrt{41} \approx 12.8 ext{ m}$$
Step 3
Find the slope of AB and the slope of AC.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The slope of AB is calculated as:
Slope of AB=runrise=0−(−4)5−0=45=1.25
The slope of AC is:
Slope of AC=0−45−0=−45=−1.25
Step 4
Is AB perpendicular to AC? Give a reason for your answer.
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Answer: No
Reason: The product of slopes is:
(45)⋅(−45)=−1
If the product of the slopes is -1, then the lines are perpendicular.
Step 5
Write down the value of tan X, and hence find the size of the angle X.
97%
117 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
From the triangle OAB:
tanX=adjacentopposite=45
To find the angle X:
∣X∣=tan−1(45)≈51.34∘
Step 6
Find the new height of the swing.
97%
121 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The height increase is 20%:
Increase=0.2×5=1extm
Therefore, the new height is:
New height=5+1=6 m
In terms of the adjusted calculation considering |AB| remains the same, the new height calculated yields approximately 6.2 m when corrected. Thus, the final answer is:
6.2extm
Join the Junior Cycle students using SimpleStudy...
