At least, it is for me :(
Triangle ABC is isosceles with segment AC congruent to BC. A (2,5), B (-2,1), and C(4,y). Find y.
How do I do this? :( Can someone please explain?
2007-01-21 12:29:57 · 15 answers · asked by 2 days after my B day :) 2 in Science & Mathematics ➔ Mathematics
Can someone please explain how to do it though? :)
2007-01-21 12:35:55 · update #1
distance(AC) = distance(BC) ... (distance formula for two points)
sqrt[(4-2)^2+(y-5)^2] = sqrt[(4-(-2))^2+(y-1)^2]
(4-2)^2+(y-5)^2 = (4-(-2))^2+(y-1)^2
4 + y^2 - 10y +25 = 36 + y^2 -2y + 1
8y = -8
y = -1
2007-01-21 12:36:09 · answer #1 · answered by Joe Mkt 3 · 1⤊ 0⤋
Joe Mkt gave the correct solution - without an explaination. Because the triagle is isosceles we know that 2 sides are the same length. We are told that those two sides are AC and BC. So Joe set up the equation to make the two lengths equal and then solved for y.
2007-01-21 12:40:54 · answer #2 · answered by rscanner 6 · 0⤊ 0⤋
basically wat i did is plot the 2 first points. that gives u line AB. ok so nw that u kno its isosceles, that means the 3rd point is equal distance from BOTH of the other points (because the lines have to be the same length...so i put a small dot where the lines meet if u make a right angle... take the one point and make a line down and the other and make a line across and it shows a intersection
take the point diagonally (bottom-right) until it lies on the x-axis-value-of-4 line... and theres your point.
i'll be honest, i dont think to a process, but i think logically... so if ur teacher requires a specific way to o it... this is not the best way... bt its the easiest if u dont know exactly what ur doing
2007-01-21 12:51:41 · answer #3 · answered by Anonymous · 0⤊ 0⤋
ok first you plot the coordinates on a grid. (over (left or right) then up. the only way I know to solve it is by checking length. they must have the same length to be congruent. Pick a spot on the y axis. measure them, and keep doing that until they are the same. (make sure the graph is on graph paper).
You should get y=-1
Since this might not be the best way, I would check with a teacher, or look it up in a book to go over it for a better explanation.
2007-01-21 12:46:57 · answer #4 · answered by skateKad47 3 · 1⤊ 0⤋
the answer is (4,-1)
i did this by first graphing the triangle on a piece of graph paper and then i knew that C was at (4,something) so i tried (4,0) and plugged it into the distance formula which is d= (the square root of ) (x2-x1)squared + (y2-y1)squared. i just kept trying until i found that AC and BC are the same length when C is at (4,-1)
i solved your problem but i don't know if i helped you understand how i got it
2007-01-21 12:45:36 · answer #5 · answered by Sophie 1 · 0⤊ 0⤋
I'm sure I can do it, I've got it roughly graphed, and from there I'd use trigonometry to get the 2 sides AC and BC equal length. But I'm hopeless at explaining how to go about it.
2007-01-21 12:39:41 · answer #6 · answered by Anonymous · 0⤊ 0⤋
AC^2=(4-2)^2+(y-5)^2
BC^2=(4--2)^2+(y-1)^2 since AC=BC
2^2+(y-5)^2=6^2+(y-1)^2
4+y^2-10y+25=36+y^2-2y+1 subtract y^2-10 from each side
4+25=36+8y+1 subtract 37 from each side
-8=8y
y=-1
C(4, -1)
2007-01-21 12:47:17 · answer #7 · answered by yupchagee 7 · 0⤊ 0⤋
OK..
Map the 2,5 as one point (Make a dot at that point on your map)
Map -2,1 as the next point (Make another dot at that point on your map)
Now for your last point-
Congruent means exact same size and shape.
Also, see if you can use anything on this site:
http://argyll.epsb.ca/jreed/math9/strand3/triangle_congruent.htm
2007-01-21 12:37:22 · answer #8 · answered by Anonymous · 0⤊ 0⤋
2+3=chair
2007-01-21 12:32:01 · answer #9 · answered by Anonymous · 0⤊ 0⤋
Draw it on an accurate x-y plane. Or, if you want to solve it mathematically, Each leg has the same length. Use the distance formula
2007-01-21 12:36:46 · answer #10 · answered by davidosterberg1 6 · 0⤊ 0⤋