Triangles are formed by the intersection of the lines `y = x` , `y = 2x` , `y = -2x` and `y = -4` . Solve tringles ABD and ABC.

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lemjay | High School Teacher | (Level 3) Senior Educator

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To start, graph the equations.

(Note: Blue-y=x, Red-y=2x, Green=y=-2x, Purple-y=-4.)

Base on the graph, the lines form two triangles. 

The blue, red and purple lines form a traingle at the left. Let this be ABD.

Base on the graph, the purple line intersects with the blue line at (-4,-4). It too intersects with the red line at (-2, 4). While the red and blue lines meet at point (0,0).

Hence, the intersection points (-4,-4) , (-2,-4) and (0,0) are the vertices of the triangle ABD, formed by blue (y=x), red (y=2x)  and puple (y=-4) lines.

Morveover, the red, green and purple lines formed another triangle at the right.

The red intersects with the green at (0,0). It too intersecst with the purple at (-2,-4). And the green and purple meet at (2,-4).

Hence, the intersection points (0,0) , (-2,-4) and (2,-4) are the vertices of the triangle ABC, formed by the red line (y=2x), gree line (y=-2x) and the purple line (y=-4).

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