Right-angled triangle

Determine point C so that triangle ABC is right-angled and isosceles with hypotenuse AB, where A[4,-6], B[-2,10]

Correct answer:

x1 =  5
y1 =  -16
x2 =  -5
y2 =  16

Step-by-step explanation:

A=(3,−6) B=(−2,10)  c=dist(A,B)=∣AB∣=(Ax​−Bx​)2+(Ay​−By​)2​=(3−(−2))2+((−6)−10)2​=281​≐16.7631  x0​=2Ax​+Bx​​=23+(−2)​=21​=0.5 y0​=2Ay​+By​​=2(−6)+10​=2  C1​=(x1​,y1​) C2​=(x2​,y2​)  x1​=Ax​−Bx​=3−(−2)=5
y1​=Ay​−By​=(−6)−10=−16
x2​=Bx​−Ax​=(−2)−3=−5
y2​=By​−Ay​=10−(−6)=16   Verifying Solution:   C=(5,−16) D=(−5,16)  x2​=dist(C,D)=∣CD∣=(Cx​−Dx​)2+(Cy​−Dy​)2​=(5−(−5))2+((−16)−16)2​=2 281​≐33.5261

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Tips for related online calculators
See also our right triangle calculator.
Calculation of an isosceles triangle.
See also our trigonometric triangle calculator.

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