Question

line m passes through points x and y. line n passes through points x and z. if m and n have equal slope, what can you conclude about points x, y, and z? explain. choose the correct answer below. a. points x, y, and z are the same point. since a line is defined by a point and a slope, the fact that lines m and n have the same slope and both pass through x means that lines m and n must be the same line or \\(\overrightarrow{xy}\cong\overrightarrow{xz}\cong\overrightarrow{yz}\\). by using the multiplication property of equality on \\(\overrightarrow{xy}\cong\overrightarrow{xz}\\), it can be shown that y = z. similar reasoning shows that x = y. by applying the transitive property of equality, x = y = z. b. y and z are on the opposite sides of x. since a line is defined by a point and a slope, the fact that lines m and n have the same slope and both pass through x means that line m which can be written as \\(\overrightarrow{yx}\\) and line n which can be written as \\(\overrightarrow{xz}\\) must be the same line. note that \\(\overline{yx}\\) is on \\(\overrightarrow{yx}\\) and \\(\overline{xz}\\) is on \\(\overrightarrow{xz}\\). therefore, by the segment addition postulate, \\(\overline{yx}+\overline{xz}=\overline{yxz}\\). c. y and z are the same point. since a line is defined by a point and a slope, the fact that lines m and n have the same slope and both pass through x means that line m which can be written as \\(\overrightarrow{xy}\\) and line n which can be written as \\(\overrightarrow{xz}\\) must be the same line or \\(\overrightarrow{xy}\cong\overrightarrow{xz}\\). by the segment addition postulate, x + y = x + z. therefore, by the addition property of equality, y \\(\cong\\) z. d. points x, y, and z are collinear. since a line is defined by a point and a slope, the fact that lines m and n have the same slope and both pass through x means that lines m and n must be the same line. as a result, z lies on line m.

Explanation:

Explicación:

Paso1: Recordar la definición de línea

Una línea se define por un punto y una pendiente. Las líneas m y n tienen la misma pendiente y pasan por el punto X.

Paso2: Analizar la relación entre las líneas

Si dos líneas tienen la misma pendiente y pasan por el mismo punto, entonces son la misma línea.

Paso3: Concluir sobre los puntos

Como m y n son la misma línea y pasan por X, Y y Z, los puntos X, Y y Z son colineales.

Respuesta:

D. Puntos X, Y, y Z son colineales. Since a line is defined by a point and a slope, the fact that lines m and n have the same slope and both pass through X means that lines m and n must be the same line. As a result, Z lies on line m.

Answer:

Explicación:

Paso1: Recordar la definición de línea

Una línea se define por un punto y una pendiente. Las líneas m y n tienen la misma pendiente y pasan por el punto X.

Paso2: Analizar la relación entre las líneas

Si dos líneas tienen la misma pendiente y pasan por el mismo punto, entonces son la misma línea.

Paso3: Concluir sobre los puntos

Como m y n son la misma línea y pasan por X, Y y Z, los puntos X, Y y Z son colineales.

Respuesta:

D. Puntos X, Y, y Z son colineales. Since a line is defined by a point and a slope, the fact that lines m and n have the same slope and both pass through X means that lines m and n must be the same line. As a result, Z lies on line m.