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anonymous

  • 4 years ago

ABCD is a square where A is the point (0,2) and C is the point (8,4). AC and BD are diagonals of the square and they intersect at E. Find the coordinates of B and D. Do you have any method other than using a vector

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  1. amistre64
    • 4 years ago
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    yes, but its complicated :)

  2. anonymous
    • 4 years ago
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    could you show me? thx alot!

  3. amistre64
    • 4 years ago
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    since a square has diags that are perp to each other; we need 2 lines that meet in the middle of AC

  4. amistre64
    • 4 years ago
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    the slope of a line is the important part here; once we know the slope of the line from A to C we can determine other things

  5. amistre64
    • 4 years ago
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    the slope of a line is found by a slope formula:\[m=\frac{y1-y2}{x1-x2}\] but i tend to step it out. 1) subtract the points 2) stack y/x

  6. amistre64
    • 4 years ago
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    C (8,4) -A (0,2) ------- 8,2; stack y/x: 2/8 = 1/4 for our slope

  7. amistre64
    • 4 years ago
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    perp slopes have the habit of being the negative reciprocal of each other. m1*m2 = -1

  8. amistre64
    • 4 years ago
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    perp slope for th eline from B to D is then: -4/1

  9. amistre64
    • 4 years ago
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    we need a common point for these to meet at, which is the middle of the square and hence E the midpoint is just the average of 2 other points. Add the points and divide by 2 C (8,4) +A (0,2) -------- (8,6)/2 = (4,3) as out point for E

  10. amistre64
    • 4 years ago
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    |dw:1327673742761:dw|

  11. amistre64
    • 4 years ago
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    this is what weve got drawn up in out heads, or on paper

  12. amistre64
    • 4 years ago
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    i know, this is where I had a brillant notion last time ... and I just remembered it :)

  13. amistre64
    • 4 years ago
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    think of a pinwheel ....

  14. amistre64
    • 4 years ago
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    |dw:1327674432861:dw|

  15. amistre64
    • 4 years ago
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    our x and y parts for A to E are going to be swapped and negated for the perp from B to E

  16. amistre64
    • 4 years ago
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    |dw:1327674563395:dw|

  17. amistre64
    • 4 years ago
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    we know to go from A to E is over 4 and up 1 (x=4, y=1) these are the distances needed for the rest of them as well right? just perp them (x=1, y=-4) is our directions from E to D (x=-1, y=4) is our directions from E to B

  18. amistre64
    • 4 years ago
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    E (4,3) E (4, 3) +(-1,4) + (1,-4) ------ -------- B (3,7) D (5,-1)

  19. amistre64
    • 4 years ago
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    that should clean up the right path a little better :)

  20. anonymous
    • 4 years ago
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    i kind of get it from the pinwheel ting

  21. anonymous
    • 4 years ago
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    ok thx:)

  22. amistre64
    • 4 years ago
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    the pinwheel thing is a very good visual to guide us :)

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