Given the vertices of a triangle as A(2, 5), B(4, 6) and C(3, 1).
a.) A transformation, R_x-axis means that the vertices of the rectangle were reflected across the x-axis.
When a point on the coordinate axis is refrected across the x-axis, the sign of the y-coordinate of the point changes.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule R_x-axis are A'(2, -5), B'(4, -6), C'(3, -1)
b.) A transformation, R_y = 3 means that the vertices of the rectangle were reflected across the line y = 3.
When a point on the coordinate axis is refrected across the a horizontal line, the distance of the point from the line is equal to the distance of the image of the point from the line.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule are A'(2, 1),
B'(4, 0), C'(3, 5)
c.) A transformation, T<-2, 5> means that the vertices of the rectangle were shifted 2 units to the left and 5 units up.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<-2, 5> are A'(0, 10),
B'(2, 11), C'(1, 6).
d.) A transformation, T<3, -6> means that the vertices of the rectangle were shifted 3 units to the right and 6 units down.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<3, -6> are A'(5, -1),
B'(7, 0), C'(6, -5).
e.) A transformation, r(90°, o) means that the vertices of the rectangle were rotated 90° to the right about the origin.
When a point on the coordinate axis is rotated about the origin b 90°, the quadrant of the point changes to the right with the x-value and the y-value of the point interchanging.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule r(90°, o) are A'(5, -2),
B'(6, -4), C'(1, -3)
Answer:
14 units
Step-by-step explanation:
The perimeter of a figure is the sum of the lengths of all the sides.
Here, we know that ABCD is a rectangle, so by definition, AB = CD and AD = BC. We also are given that AB = 3y + 3 and BC = 2y, which means that:
AB = CD = 3y + 3
AD = BC = 2y
Adding up all the side lengths and setting that equal to the perimeter, which is 76 units, we get the expression:
AB + CD + AD + BC = 76
(3y + 3) + (3y + 3) + 2y + 2y = 76
10y + 6 = 76
10y = 70
y = 7
We want to know the length of AD, which is written as 2y. Substitute 7 in for y:
AD = 2y = 2 * 7 = 14
The answer is thus 14 units.
<em>~ an aesthetics lover</em>