Now we need to simplify underneath the radical, starting with the parentheses, so that equals the square root of, (can add the inverse) 1 plus 2 is 3, squared, plus, 3 minus 2 is 1, squared, that equals the square root of 3 squared is 9, plus, 1 squared is 1, so that equals the square root of 10. First, I want to find the distance from A to B, so that’s the square root of x_2 is 1, minus x_1 is negative 2, squared, plus, y_2 is 3, minus y_1 is 2, squared. In one point, like point A, you couldn’t call one coordinate x_1 and then the other one y_2, so as long as you don’t mix it up like that, you can label any of the points x_1, y_1, x_2, y_2, it doesn’t matter. We’re going to use the distance formula, which is distance equals the square root of x_2 minus x_1, squared, plus, y_2 minus y_1, squared, (and I’ve already put the labels on all of my points) and it doesn’t matter which point you call x_1, y_1, or x_2, y_2, as long as you’re consistent. In order to tell if they’re congruent, I’m going to find the distance between the points, and if the distances between the points are the same, then that means that those segments are congruent.
That means that I need to show that both pairs of my adjacent sides are congruent, or that I have two pairs of adjacent sides that are congruent. I’m going to use the first method to determine if this quadrilateral, ABCD, is a kite. You can use either of these things to determine if a quadrilateral is a kite. A kite also has perpendicular diagonals, where one bisects the other. A kite is a quadrilateral with two pairs of adjacent sides, congruent.
Determine if quadrilateral ABCD is a kite.
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