Question

(11) triangle abc has coordinates: a(2,7) b(8,3) and c(2,2) which are the coordinates of the image of triangle abc after a reflection across the y- axis? 12) the coordinates of δabc are: a(8,1) b(6,8) and c(8,3). the pre-image of δ is reflected across the x axis what are the coordinates after the reflection? a( , ) b( , ) c ( , ) 13) 6th grade a coordinate plane can be used to show the distance, in units, between two locations. the location of jack’s house and a store are listed below. jack’s house is located at (-7, -8). the store is located at (-7, -4). what is the distance, in units, between jack’s house and the store? show your work! 14) 6th grade what order pair is the location of a point that is the reflection of the point (-4,6) over the x - axis? a) (4,6) b) (-4 -,6) c) (6, -4) d) (-6,4) 15) write the rule of the transformation image of a coordinate grid with a polygon and its image 16) reflect abcd across the y-axis and label the image. image of a coordinate grid with quadrilateral abcd

Explanation:

12)

Step1: Regla de reflexión en el eje x

La regla para reflejar un punto \((x,y)\) en el eje \(x\) es \((x,-y)\).

Step2: Aplicar la regla a cada punto

• Para \(A(8,1)\): \(A'(8,- 1)\)
• Para \(B(6,8)\): \(B'(6,-8)\)
• Para \(C(8,3)\): \(C'(8,-3)\)

Step1: Identificar la fórmula de distancia en el eje y

Como las coordenadas \(x\) de Jack's house \((-7,-8)\) y la tienda \((-7,-4)\) son iguales (\(x = - 7\)), la distancia entre ellos se calcula como \(d=\vert y_2 - y_1\vert\).

Step2: Sustituir los valores

Tomando \(y_1=-8\) y \(y_2 = - 4\), entonces \(d=\vert-4-(-8)\vert=\vert-4 + 8\vert=\vert4\vert = 4\)

Step1: Aplicar la regla de reflexión en el eje x

La regla para reflejar un punto \((x,y)\) en el eje \(x\) es \((x,-y)\).

Step2: Sustituir \(x=-4\) y \(y = 6\)

Para el punto \((-4,6)\), la reflexión es \((-4,-6)\)

Answer:

\(A'(8,-1)\), \(B'(6,-8)\), \(C'(8,-3)\)

13)