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How do I know that if line AB = AC, there'll be an isosceles?

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1. Part C is the one I don't understand.

How am I supposed to take AC = AB? Does it mean that the gradients are the same (well, considering the answer, no, but still)? The lines are the same? What is the question implying? I know that the lines would form an isosceles, but how am I supposed to know that just out of nothing?
2. AC = AB just means the length of the lines are the same, not their gradients
3. I'm not sure if you've completed this or not, but here's some help anyway!

From part b, you should have found that AB has length of root 41.
You do part C in a similar way. So, you know A is (7,4) and C is (2,t).

AC^2 = (t-4)^2 + (2-7)^2.

And you are given that AC = AB. So, AC is also equal to root 41.
So, ((root 41))^2 = (t-4)^2 + (2-7)^2.
Can you expand this for me and see what you get t as being?

Once you've done that, i'll help you with part d) if you need it.

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