Triangle DEF, with vertices D(9,-8), E(8,-3), and F(2,-5), is drawn inside a rectangle,
1 answer:
The area of the triangle DEF is 2 square units
<h3>How to determine the area?</h3>The given parameters are:
D(9,-8), E(8,-3), and F(2,-5),
The area of the triangle is calculated using:
Area = 0.5|x1 * (y2 -y3) + x2 * (y1 -y3) + x3 * (y2 -y1) |
This gives
Area = 0.5|9 * (-3 + 5) + 8 * (-8 + 5) + 2 * (-3 + 8) |
Evaluate
Area = 0.5|4|
Expand
Area = 2
Hence, the area of the triangle DEF is 2 square units
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Answer:
The vertices of image are A'(0,0), B'(-1,-5) and C'(4,-5). The graph of image and preimage is shown below.
Step-by-step explanation:
From the given figure it is noticed that the vertices of triangle ABC are A(0,0), B(1,5) and C(-4,5).
If a figure rotated at 180º about the origin, then
The vertices of image are
Therefore the vertices of image are A'(0,0), B'(-1,-5) and C'(4,-5).
The graph of image and preimage is shown below.
Answer:
(a)
(b) The graph is shown below.
(c) Seiji earned $ 210 and Gavin earned $ 240.
Step-by-step explanation:
Given:
Sum of earnings of Seiji and Gavin = $ 450
Gavin earns $ 30 more that that of Seiji.
(a)
So, as per question, if s and g are the amounts earned by Seiji and Gavin respectively, then;
(b)
The graph is plotted using the x and y intercepts of each line.
For the line, , the x intercept is at
. So, x intercept is (450,0). Similarly, the y intercept is when s=0, which is (0,450). Draw a line passing through these two points. The red line represents
.
We follow the same process to plot the next line. The x intercept is at (-30,0) and y intercept is at (0,30). Draw a line passing through these two points. The blue line represents .
The graph is shown below.
(c)
From the graph, the point of intersection of the two lines gives the earnings of each of the persons.
The value of the point of intersection is the earning of Seiji which is $ 210 and the
value is the earning of Gavin which is $ 240 as shown in the graph.
Therefore, Seiji earned $ 210 and Gavin earned $ 240.
