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Unsure on how to find the exact length of AB (quadratic simultaneous equations).

Howdy :smile:.

I don't know how to get the answer on the attached question.

I solved them as quadratic simultaneous equations to get (3,-3) and (5, 1) as the points of intersection.

How do I find the exact length of AB?

Thanks
Quads.jpg40.1KB
Reply 1
Avatar for Zacken
Zacken
22
Original post by jojo55
Howdy :smile:.

I don't know how to get the answer on the attached question.

I solved them as quadratic simultaneous equations to get (3,-3) and (5, 1) as the points of intersection.

How do I find the exact length of AB?

Thanks


You should know that to find the distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) we have the distance as d=(x1−x2)2+(y1−y2)2d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}.
Reply 2
Avatar for alesha98
alesha98
4
Original post by jojo55
Howdy :smile:.

I don't know how to get the answer on the attached question.

I solved them as quadratic simultaneous equations to get (3,-3) and (5, 1) as the points of intersection.

How do I find the exact length of AB?

Thanks


Yes your solution of the simultaneous equation is right, So now you have two coordinates. Use the distance formula to find the length of AB.
Reply 3
Avatar for jojo55
jojo55
OP
11
Original post by Zacken
You should know that to find the distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) we have the distance as d=(x1−x2)2+(y1−y2)2d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}.


Original post by alesha98
Yes your solution of the simultaneous equation is right, So now you have two coordinates. Use the distance formula to find the length of AB.


Thanks for the help :biggrin:.

I didn't know that equation.

I can see that it comes to SQRT(4 + 16). Which comes to the answer given.
Reply 4
Avatar for Zacken
Zacken
22
Original post by jojo55
Thanks for the help :biggrin:.

I didn't know that equation.

I can see that it comes to SQRT(4 + 16). Which comes to the answer given.


It's the pythagoras equation with coordinates. If you drew the given points on a graph and sketched a triangle, you would see that the distance between the two points is the hypotenuse of the triangle with height y1 - y2 and base x1 - x2. Hence the equation.

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