You are watching: Points a(-2, 4), b(1, 3), c(4, -1) and d form a parallelogram. what are the coordinates of d?
Click here to watch ALL problems on Geometry indigenous ProblemsQuestion 797588: clues A (-2, 4) , B (1, 3) , C (4,-1) and D type a parallelogram. What room the coordinates? found 2 remedies by josgarithmetic, MathTherapy:Answer by josgarithmetic(36162) (Show Source): You can put this equipment on your website! EDIT: use OF GRAPH provided THE exactly ANSWER. View Below..... At least you must put A, B, and C ~ above graph paper, and also decide whereby to put D. Then you have the right to use basic coordinate geometry of lines and also the street formula, maybe, to find the coordinates needed because that D. Since you want a parallelogram, you understand that there room two pair that parallel lines, you recognize two clues define any kind of line...The concern seems slightly open-ended. Arbitrarily picking BC as one of the sides, and abdominal as the other side, the two sides conference at point B, the slope because that the next BC is .The parallel needs another side, AD, which has actually the exact same slope, -4/3, as line BC. Keep in mind too that line ad obviously contains suggest A. We have the works with for point A, gift (-2,4). We deserve to use the POINT-SLOPE form for a direct equation to gain line AD.Line advertisement is , where m is slope, (u,v) is a allude known ~ above the line.-------(MISTAKE action HERE. SHOULD have actually BEEN , and then ), heat AD.You also want to know line DC, since this will intersect line AD, at point D. Line DC will must be parallel to heat AB, so us must discover slope because that AB, and use known point C in POINT-SLOPE type for a heat to find line DC.Slope abdominal muscle is slope DC, , this slope. Which is generalized point-slope form; see above., line DC.FINALLY, at what allude D, execute lines ad and DC intersect?Equating your formulas because that y,Use one of two people equations to uncover y indigenous the now found x:DC, may possibly be a mistake somewhere there, but again, usage a gridded sheet of graph file to check and make a good visual estimate, in ~ least. My calculations here seem to show , ----------------------------A failure MUST have been made in the above work. I just tried the point out on graph paper, and also it seems, allude D should be at (1,0). Shot my advice generally, but be careful, and suspicious of the values I picked and also calculated. My graph appears to show, slope for abdominal muscle is -1/3, and also slope because that BC is -4/3; for this reason those lot are good.BRIEF an introduction OF SOLUTION an approach SUCCESSFUL: do the efforts again using symbolism and also occupychristmas.org. Better. Slope abdominal is -1/3.Slope of BC is -4/3. Suggest Slope kind was used next. General allude (u,v), kind is y-v=m(x-u).Line ad parallel come BC. Line advertisement uses slope -4/3 and point A(-2,4). Resulting equation in standard form is 4x+3y=4.Line DC parallel to AB. Heat DC supplies slope -1/3 and allude C(4,-1). Resulting equation in standard form is x+3y=1.Elimination technique on the mechanism of standard form equations gives x=1 and y=0. PERFECT. Suggest is D(1,0).
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Price by MathTherapy(9840) (Show Source): You can put this solution on her website! clues A (-2, 4) , B (1, 3) , C (4,-1) and D form a parallelogram. What are the coordinates?Coordinates the D: (1, 0)