Question

A vilikg club wants to build a mati-1nade lake. A metnber of the club mapped the bocusdary of the lake con a coordinate system, with x atid y boeh mensured in miles. Esing the clabbouse as the origin, with Noth alang the poeitive traxis and East along the positive Inaxis, she found that the curve x²+xy+y² −13x−14y=−34 perfectly follows the lake s boundaries.

(a) Interpret the point (1,2) in the context of the situation.

Answer 1

In the context of the man-made lake's coordinate system, the point (1,2) marks a location on the lake's boundary which is 1 mile East and 2 miles North from the clubhouse at the origin.

Step-by-step explanation:

In the context of the situation described, the point (1,2) would represent a specific location on the boundary of the man-made lake that the hiking club wishes to create. Having established a coordinate system with the clubhouse at the origin, the point with coordinates (1 mile, 2 miles) indicates a location that is 1 mile to the East (along the positive x-axis) and 2 miles to the North (along the positive y-axis) from the clubhouse. Given that the lake's boundary is defined by the curve x²+xy+y² −13x−14y=−34, the point (1,2) lies on this curve and thus marks the lake's edge at that exact position in the coordinate system provided.