Answer: Please view the picture below
Step-by-step explanation:
This material should not be too difficult. Please study more. :)
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<h3>Answer: 42 square units</h3>
Check out the attached images below. In figure 1, I plotted the four points given as A, B, C, D; then connected them to form a rectangle.
Figure 2 shows 4 more points E, F, G, H made so that a larger rectangle forms. This newer larger rectangle entirely encloses the first rectangle. The idea is to find the area of the larger rectangle, and subtract off the areas of the four triangular pieces shown in figure 3. These images are attached below.
area of rectangle EFGH = base*height = 10*10 = 100
area of triangle ABE = base*height/2 = 3*3/2 = 4.5
area of triangle ADH = base*height/2 = 7*7/2 = 24.5
area of triangle CGD = base*height/2 = 3*3/2 = 4.5
area of triangle FCB = base*height/2 = 7*7/2 = 24.5
the four triangles have areas that add up to 4.5+24.5+4.5+24.5 = 58
Subtract this from the area of rectangle EFGH to get 100-58 = 42
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alternatively, you can find the distance from A to B getting roughly 4.24264 (use the distance formula). The distance from B to C is roughly 9.89949
Multiply those two values: 4.24264 * 9.89949 = 41.9999722536 which rounds to 42. There's rounding error based on the fact that the previously mentioned decimal values are approximate.
Answer:
Step-by-step explanation:
A line that is perpendicular to a reference line will have a slope that is the negative inverse of the reference line.
In this case, the reference line is y = -x - 1. It has a slope of -1. The negative inverse of this would be -(1/-1) = 1.
We can then write:
y = mx + b
y = 1x + b
To find b, enter the one given point that lines on the line, (-4,2).
y = 1x + b
y = 1x + b for (-4,2)
2 = 1(-4) + b
b = 6
The equation becomes y = x + 6
See attached.
