Question

name date geometry unit 1 lesson 1 - 3 practice problems
3 the diagram was constructed with straightedge and compass tools. points a, b, c, d, and e are all on line segment cd. name a line segment that is half the length of cd. explain how you know.
4 this diagram was constructed with straightedge and compass tools. a is the center of one circle, and c is the center of the other.
a. the two circles intersect at point b. label the other intersection point e.
b. how does the length of segment ce compare to the length of segment ad?

1. an equation is shown.

y = \frac{1}{2}x+\frac{3}{4}
select all of the points that are contained in the graph of the equation.
a. (0,\frac{1}{2})
b. (0,\frac{3}{4})
c. (\frac{3}{4},0)
d. (\frac{1}{2},\frac{3}{4})
e. (\frac{1}{2},1)

Explanation:

Explicación paso a paso:

Paso 1: Sustituir puntos en la ecuación

Para cada punto $(x,y)$, sustituimos $x$ y $y$ en $y=\frac{1}{2}x+\frac{3}{4}$.

Paso 2: Analizar punto A $(0,\frac{1}{2})$

Sustituimos $x = 0$ y $y=\frac{1}{2}$: $\frac{1}{2}=\frac{1}{2}(0)+\frac{3}{4}=\frac{3}{4}$, falso.

Paso 3: Analizar punto B $(0,\frac{3}{4})$

Sustituimos $x = 0$ y $y=\frac{3}{4}$: $\frac{3}{4}=\frac{1}{2}(0)+\frac{3}{4}$, verdadero.

Paso 4: Analizar punto C $(\frac{3}{4},0)$

Sustituimos $x=\frac{3}{4}$ y $y = 0$: $0=\frac{1}{2}(\frac{3}{4})+\frac{3}{4}=\frac{3 + 6}{8}=\frac{9}{8}$, falso.

Paso 5: Analizar punto D $(\frac{1}{2},\frac{3}{4})$

Sustituimos $x=\frac{1}{2}$ y $y=\frac{3}{4}$: $\frac{3}{4}=\frac{1}{2}(\frac{1}{2})+\frac{3}{4}=\frac{1}{4}+\frac{3}{4}=1$, falso.

Paso 6: Analizar punto E $(\frac{1}{2},1)$

Sustituimos $x=\frac{1}{2}$ y $y = 1$: $1=\frac{1}{2}(\frac{1}{2})+\frac{3}{4}=\frac{1 + 3}{4}=1$, verdadero.

Respuesta:

B. $(0,\frac{3}{4})$, E. $(\frac{1}{2},1)$

Answer:

Explicación paso a paso:

Paso 1: Sustituir puntos en la ecuación

Para cada punto $(x,y)$, sustituimos $x$ y $y$ en $y=\frac{1}{2}x+\frac{3}{4}$.

Paso 2: Analizar punto A $(0,\frac{1}{2})$

Sustituimos $x = 0$ y $y=\frac{1}{2}$: $\frac{1}{2}=\frac{1}{2}(0)+\frac{3}{4}=\frac{3}{4}$, falso.

Paso 3: Analizar punto B $(0,\frac{3}{4})$

Sustituimos $x = 0$ y $y=\frac{3}{4}$: $\frac{3}{4}=\frac{1}{2}(0)+\frac{3}{4}$, verdadero.

Paso 4: Analizar punto C $(\frac{3}{4},0)$

Sustituimos $x=\frac{3}{4}$ y $y = 0$: $0=\frac{1}{2}(\frac{3}{4})+\frac{3}{4}=\frac{3 + 6}{8}=\frac{9}{8}$, falso.

Paso 5: Analizar punto D $(\frac{1}{2},\frac{3}{4})$

Sustituimos $x=\frac{1}{2}$ y $y=\frac{3}{4}$: $\frac{3}{4}=\frac{1}{2}(\frac{1}{2})+\frac{3}{4}=\frac{1}{4}+\frac{3}{4}=1$, falso.

Paso 6: Analizar punto E $(\frac{1}{2},1)$

Sustituimos $x=\frac{1}{2}$ y $y = 1$: $1=\frac{1}{2}(\frac{1}{2})+\frac{3}{4}=\frac{1 + 3}{4}=1$, verdadero.

Respuesta:

B. $(0,\frac{3}{4})$, E. $(\frac{1}{2},1)$