Question

Indicate the equation of the given line in standard form, writing the answer in the equation box below. The line containing the longer diagonal of a quadrilateral whose vertices are A(2, 2), B(-2,-2), C(1, -1), and D(6,4).

a) x - y = 0
b) 2x - 2y = 0
c) x + y = 0

Answer 1

The equation of the line containing the longer diagonal of the quadrilateral in standard form is x - 2y = -2.

Step-by-step explanation:

To find the equation of the line containing the longer diagonal of the quadrilateral, we can find the slope of the line using the coordinates of the diagonal. The longer diagonal of the quadrilateral is formed by the points A(2, 2) and D(6, 4). The slope of the line can be found using the formula: slope = (y2 - y1) / (x2 - x1). Substituting the coordinates of A and D, we get: slope = (4 - 2) / (6 - 2) = 2 / 4 = 1/2.

Now that we have the slope, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. We'll use point A(2, 2) as (x1, y1) and the slope 1/2. Plugging in the values, we get: y - 2 = 1/2(x - 2). Expanding and rearranging the equation, we get: 2y - 4 = x - 2. Finally, we can rewrite the equation in standard form by moving all terms to one side: x - 2y = 2 - 4. The equation of the line containing the longer diagonal of the quadrilateral in standard form is x - 2y = -2.