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^how do you do this question? I don't have the answer nor explanation :(</p>
<p>Let A be the point (0,5). Point B is then (5,7). The slope of this line is then (7-5)/(5-0)=2/5. Thus the equation for line l is y=2x/5+5. In the diagram it is clear that the x coordinate for point C is 12. Plug 12 into the equation and we see that y=2(12/5)+5=24/5+25/5=49/5. Thus, x=49/5.</p>
<p>Another solution involves triangles. Imagine two right triangles, one whose hypotenuse is AB (creating triangle 1) and the other whose is BC (creating triangle 2). </p>
<p>Triangle 1 has legs of 5 and 2 (by 7-5). Triangle 2 has legs of 7 and x-7 (by similar thinking). </p>
<p>The triangles are similar because they explicitly share two angles (the right angles and the angles created by the invariably sloped line’s intersection), which affirms similarity. So we can relate:
5/2=7/(x-7)
5/2x-35/2=7
5x-35=14
5x=49
x=49/5</p>