Question

Let r: x - y 5 = 0. Determine a general equation of the line s parallel to the line r, which forms an isosceles triangle with area 8 with the line x = 5 and the Ox axis.

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Corbin

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The x-axis and x=5 intersects at (5,0). If the area of the triangle is 8, then the base is 4 units and the height is 4 units as well. From these, we can obtain the other vertices of the triangle. They are on (1,0) and (5,4). Using the two point form:
y=\frac{y_2-y-1}{x_2-x_1}(x-x_1)+y_1
y=\frac{4-0}{5-1}(x-1)+0
y=1(x-1)
y=x-1
Writing in the general form on a line x-y-1=0

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