On the coordinate plane, the segment from A(–4,–3) to B(6,–3) forms one side of △ABC. The triangle has an area of 25 square units. Select all of the points where C could be.(–1,2)(–1,–8)(9,1)(–1,1)Submit
Question
On the coordinate plane, the segment from A(–4,–3) to B(6,–3) forms one side of △ABC. The triangle has an area of 25 square units. Select all of the points where C could be.(–1,2)(–1,–8)(9,1)(–1,1)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 AB, which has a length of 10 units (6 - (-4)).
So, the height of the triangle is 2 * Area / base = 2 * 25 / 10 = 5 units.
The height of the triangle is the distance from point C to the line AB. Since AB lies on the line y = -3, the y-coordinate of point C must be either -3 + 5 = 2 or -3 - 5 = -8.
Therefore, the possible coordinates for point C are (-1, 2) and (-1, -8).
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