A rectangle has two opposite vertices at the points (1$$, $$2) and (5$$, $$5). If the other vertices lie on the line x $$=$$ $$3$$, then the coordinates of the other vertices are

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Infinity Learn · Accepted Answer

Let A ≡ (1$$, $$2) and C ≡ (5$$, $$5). Since the vertices B and D lie on the line x $$=$$ $$3$$, therefore, let B ≡ (3$$, $$y1) and D ≡ (3$$, $$y2).Since AC and BD bisect each other, so they have same middle pointi.e,  $$y1+y22=2+52$$ or  $$y1+y2=7$$                                 (1)Also$$, $$BD2$$ $$=$$ $$AC2$$⇒ $$(y1$$ – $$y2)2$$ $$=$$ $$(1$$ – $$5)2$$ $$+$$ $$(2$$ – $$5)2$$ $$=$$ $$25or$$ $$y1$$ – $$y2$$ $$=$$ ± $$5$$                                   $$(2)Solving$$ $$(1) and (2), we get $$y1$$ $$=$$ $$6$$, $$y2$$ $$=$$ $$1$$ or $$y1$$ $$=$$ $$1$$, $$y2$$ $$=$$ $$6Thus$$, the other vertices of the rectangle are (3$$, $$1)and$$ $$(3$$, $$6).

A rectangle has two opposite vertices at the points (1, 2) and (5, 5). If the other vertices lie on the line x = 3, then the coordinates of the other vertices are

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