![]() Let the position of the vertex A remains unchanged and C1is the new position of C.The distance of C1from A is equal toa)b)c)d)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2023 Exam.įind important definitions, questions, meanings, examples, exercises and tests below for A rectangle ABCD of dimensions r and 2r is folded along diagonal BD such that planes ABD and CBD are perpendicular to each other. Information about A rectangle ABCD of dimensions r and 2r is folded along diagonal BD such that planes ABD and CBD are perpendicular to each other. The Question and answers have been prepared Can you explain this answer? for JEE 2023 is part of JEE preparation. The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.A rectangle ABCD of dimensions r and 2r is folded along diagonal BD such that planes ABD and CBD are perpendicular to each other. Using the distance formula, Also using the distance formula, Finally, ![]() Next find point Q by solving the system of equations for and to get. ![]() Solving the system of equations for and to find point, and. The equation of is, the equation of is, and the equation of is. ~ isabelchen Solution 6 (Coordinate Bash, not as efficient as Solution 1 but it works) īecause and share the same base, the ratio is equal to the ratio of altitude of to to that of to, which is equal to : I will calculate using the ratio of area of to that of. īecause and share the same base, the ratio is equal to the ratio of the altitude of to to that of to, which is equal to : I will calculate using similar triangle, and using ratio of area of to. Since the denominator of must now be a multiple of 7, the only possible solution in the answer choices is. Labeling and, we see that turns out to be equal to. Furthermore, the ratio between the side lengths of the two triangles is. Since the opposite sides of a rectangle are parallel and due to vertical angles. Thus, we see that Solution 3 (Answer Choices) Now we can find Solution 2 (Similar Triangles)Įxtend to intersect at. įinding the intersections of and, and and gives the x-coordinates of and to be and. They are as follows:Īfter drawing in altitudes to from, , and, we see that because of similar triangles, and so we only need to find the x-coordinates of and. Next, we will find the equations of, , and. The slopes of these lines are, , and, respectively. Then, we will find the equations of the following three lines:, , and. What is the value of ?įirst, we will define point as the origin. Segments and intersect at and, respectively. Point lies on so that, point lies on so that, and point lies on so that.
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