If point ( a ) has coordinates ((x, y)), its reflection across the y-axis would change the x-coordinate to its negative, resulting in the new coordinates ((-x, y)). Therefore, the coordinates of point ( a ) after reflection across the y-axis would be ((-x, y)).
That depends on where the triangle ABC is located on the Cartesian plane for the coordinates of its vertices to be determined.
When polygon ABC-DE is translated 2 units to the right and 4 units up, each vertex of the polygon will move accordingly. This means that the x-coordinates of all vertices will increase by 2, and the y-coordinates will increase by 4. As a result, the shape and orientation of the polygon will remain unchanged, but its position on the coordinate plane will be shifted to a new location. The overall size and properties of the polygon will remain the same.
The answer depends on what ABC is!
The analytical method is far from simple:Divide the quadrilateral into two triangles, say ABC and BCD.The centroid of triangle ABC is P = [(xa+xb+xc)/3 , (ya+yb+yc)/3] where (xa,ya) are the coordinates of A and so on.Label the centroid of BCD as Q and find its coordinates in a similar way.The next step is to find the areas of the two triangles.Area (ABC) = gArea(BCD) = hThen the centroid of the whole quadrilateral is the weighted average of the coordinates of P and Q, with weights g and h.Thus, if R is the centroid of the quadrilateral, thenxr = (g*xp + h*xq)/(g+h) andyr = (g*yp + h*yq)/(g+h).If you can cut out the quadrilateral the procedure is much simpler. Suspend the quadrilateral from one corner and, using a plumb line or equivalent, mark the vertical direction. Repeat from the adjacent vertex. The two lines will meet at the centroid.
To carry triangle ABC onto itself through reflections, you can use the reflections across its medians, angle bisectors, or altitudes. Specifically, reflecting across the angle bisectors of the triangle will map each vertex to the opposite side, preserving the triangle's shape. Additionally, reflecting across the perpendicular bisectors of the triangle's sides will also result in the triangle being mapped onto itself. These reflections maintain the congruence and orientation of the triangle.
Bho
The answer will depend on the original coordinates of A: these have not been provided so neither has an answer.
answer
That depends on where the triangle ABC is located on the Cartesian plane for the coordinates of its vertices to be determined.
2 down 1 up
Find the coordinates of the vertices of triangle a'b'c' after triangle ABC is dilated using the given scale factor then graph triangle ABC and its dilation A (1,1) B(1,3) C(3,1) scale factor 3
(-5, 6)
(9, -5)
(6, -4)
It is (10, -2).
That would depend on its original coordinates and in which direction clockwise or anti clockwise of which information has not been given.
The coordinates of the point P would be definitely 3 6.