WXYZ is a trapezoid with vertices W(–1, 2), X(3, 2), Y(5, –1), and Z(–3, –1). Which is a line of symmetry with the correct justi
fication?
1 answer:
1. Plot the points in the coordinate axes as in the attached picture.
2. The trapezoid is isosceles. This can be easily checked by calculating WZ and XY by the Pythagorean theorem. Or simply by the picture.
The midpoint of W and X is at (1, 2)
The midpoint of Z and Y is at (1, -1)
the line of symmetry is the line passing through these 2 midpoints. This line is the vertical line through x=1.
Answer: axis of symmetry: line with equation x=1
justification: the pairs W,X and Z,Y are symmetrical with respect to this line
2. The trapezoid is isosceles. This can be easily checked by calculating WZ and XY by the Pythagorean theorem. Or simply by the picture.
The midpoint of W and X is at (1, 2)
The midpoint of Z and Y is at (1, -1)
the line of symmetry is the line passing through these 2 midpoints. This line is the vertical line through x=1.
Answer: axis of symmetry: line with equation x=1
justification: the pairs W,X and Z,Y are symmetrical with respect to this line
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Answer:
Los lados del triángulo rectángulo miden 3, 4 y 5, respectivamente.
Step-by-step explanation:
Un triángulo rectángulo puede ser descrito mediante el teorema de Pitágoras, para el caso de tres lados representando tres números enteros consecutivos, tenemos que:
(1)
Donde es un número natural.
A continuación, expandimos la expresión y resolvemos:
La única solución factible es . En consecuencia, los lados del triángulo rectángulo miden 3, 4 y 5, respectivamente.