Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 3 units long. Point C is on the line x = -1. If the area of triangle ABC is 6 square units, then find a possible y-coordinate of point C. Options: 5 6 7 8

The coordinate of a point is given by (x,y) where x is the horizontal distance from the origin on the x axis and y is the vertical distance from the origin.

Given Segment AB is on the line y = 2 and is 3 units long and Segment AB is on the line y = 2 and is 3 units long. The area of triangle ABC is 6 square units.

The area of a triangle = 1/2 × base × height

6 = 1/2 × 3 × height

height = (2 × 6) / 3 = 4 units

Since point C is perpendicular to line y = 2, they coordinates is either 2 + 4 = 6 or 2 - 4 = -2

The coordinate of point C is either (-1, 6) or (-1, -2)

abidemiokin abidemiokin · Answer 2 · 2022-01-14T13:06:17+01:00

The coordinate of point C is either (-1, 6) or (-1, -2)

Area of triangles and coordinates

The formula for calculating the area of a rectangle is expressed as;

A = 0.5bh

where:

b is the base of the triangle
h is the height of the triangle;

Get the height of the triagle:

6 = 0.5(3)h

6 = 1.5h

h = 6/1.5

h = 4 units

Since point C is perpendicular to line y = 2, the y-coordinates will be either (2 + 4) = 6 or (2 - 4) = -2

Hence the coordinate of point C is either (-1, 6) or (-1, -2)

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