the vertices of a triangle are p(-7, -4), q(-7, -8) and r(3, -3) name the vertices of the image reflected across the line y = x
A: P'(4, 7), Q'(8, 7), R'(3, -3)**My Answer**
B: P'(4, -7), Q'(8, -7), R'(3, 3)
C: P'(-4, -7), Q'(-8, -7), R'(-3, 3)
D: P'(-4, 7), Q'(-8, 7), R'(-3, -3)
To find the vertices of the image of the triangle reflected across the line y = x, you need to reflect each vertex individually. The line y = x is a diagonal line that passes through the origin with a slope of 1.
To reflect a point across a line, you need to determine the perpendicular distance between the point and the line, and then mirror the point on the other side of the line using that distance. Since the line y = x passes through the origin (0, 0), the perpendicular distance of any point (x, y) from the line is equal to the distance from (x, y) to the origin.
Let's apply this to each vertex:
1. P(-7, -4):
The perpendicular distance of P from the line y = x is equal to the distance from P to the origin, which can be calculated using the distance formula: d = sqrt((-7)^2 + (-4)^2) = sqrt(49 + 16) = sqrt(65).
The image of P' will be located at the same perpendicular distance from the line y = x, but on the other side. Since the line y = x passes through the origin, the image point P' will have the same x-coordinate as P and the same y-coordinate as the origin (0, 0), so P' will be (4, 7).
2. Q(-7, -8):
Similarly, Q' will have the same x-coordinate as Q and the same y-coordinate as the origin. Therefore, Q' will be (8, 7).
3. R(3, -3):
Like P and Q, R' will have the same x-coordinate as R and the same y-coordinate as the origin. Thus, R' will be (3, -3).
So the correct choice is A: P'(4, 7), Q'(8, 7), R'(3, -3).
find R' (the reflection of r)
draw the reflecting line and do the reflection