Vertices of quadrilateral ABCD: A(a;-3), B(4;5), C(-1;5), D(-2;1)
Determine the value of a if the distance from A to B and A to D is the same.
Determine the value of a if the distance from A to B and A to D is the same.
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AB = √[(4 - a)² + 8²] = √(a² - 8a + 80)
AD = √[(-2 - a)² + 4²] = √(a² + 4a + 20)
AB = AD implies that
√(a² - 8a + 80) = √(a² + 4a + 20)
a² - 8a + 80 = a² + 4a + 20
12a = 60
a = 5
AD = √[(-2 - a)² + 4²] = √(a² + 4a + 20)
AB = AD implies that
√(a² - 8a + 80) = √(a² + 4a + 20)
a² - 8a + 80 = a² + 4a + 20
12a = 60
a = 5