On the coordinate plane, the segment from E(5,3) to F(5,–3) forms one side of △EFG. The triangle has an area of 12 square units. Select all of the points where G could be.(9,5)(1,–2)(1,4)(5,–1)Submit
Question
On the coordinate plane, the segment from E(5,3) to F(5,–3) forms one side of △EFG. The triangle has an area of 12 square units. Select all of the points where G could be.(9,5)(1,–2)(1,4)(5,–1)Submit
Solution
The area of a triangle is given by the formula 1/2 * base * height. In this case, the base of the triangle is the line segment from E(5,3) to F(5,-3), which has a length of 6 units (3 - (-3)).
Given that the area of the triangle is 12 square units, we can set up the equation 1/2 * 6 * height = 12 and solve for the height. This gives us a height of 4 units.
The height of the triangle is the distance from the base to the point G. Since the base is a vertical line, the x-coordinate of G must be either 5 + 4 = 9 or 5 - 4 = 1.
Therefore, the possible points for G are (9,5) and (1,-2). The points (1,4) and (5,-1) do not satisfy the conditions for the location of G.
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