If a geometric figure with a vertex at the point Y(−4, 1)
is translated down 3 units and to the right 8 units, what are the coordinates of the translated point Y′
?(1 point)
Responses
(4,−2)
left parenthesis 4 comma negative 2 right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(4, 4)
left parenthesis 4 comma 4 right parenthesis
(−7, 9)
To translate a point down 3 units and to the right 8 units, we simply add 8 to the x-coordinate and subtract 3 from the y-coordinate.
So, the coordinates of the translated point Y' would be (4, -2).
Therefore, the correct answer is (4,−2).
Rectangle ABCD
has vertices A(−1,−2)
, B(−1,−8)
, C(−8,−8)
, and D(−8,−2)
.
The rectangle ABCD
is reflected on the x
-axis and the y
-axis. Find the coordinates of the vertices for rectangle A′B′C′D′
.(1 point)
Responses
Rectangle A′B′C′D′
has vertices A′(1,2)
, B′(1,8)
, C′(8,8)
, and D′(8,2)
.
Rectangle upper A prime upper B prime upper C prime upper D prime has vertices upper A prime left parenthesis 1 comma 2 right parenthesis , upper B prime left parenthesis 1 comma 8 right parenthesis , upper C prime left parenthesis 8 comma 8 right parenthesis , and upper D prime left parenthesis 8 comma 2 right parenthesis .
Rectangle A′B′C′D′
has vertices A′(1,−2)
, B′(1,−8)
, C′(8,−8)
, and D′(8,−2)
.
Rectangle upper A prime upper B prime upper C prime upper D prime has vertices upper A prime left parenthesis 1 comma negative 2 right parenthesis , upper B prime left parenthesis 1 comma negative 8 right parenthesis , upper C prime left parenthesis 8 comma negative 8 right parenthesis , and upper D prime left parenthesis 8 comma negative 2 right parenthesis .
Rectangle A′B′C′D′
has vertices A′(−1,2)
, B′(−1,8)
, C′(−8,8)
, and D′(−8,2)
.
Rectangle upper A prime upper B prime upper C prime upper D prime has vertices upper A prime left parenthesis negative 1 comma 2 right parenthesis , upper B prime left parenthesis negative 1 comma 8 right parenthesis , upper C prime left parenthesis negative 8 comma 8 right parenthesis , and upper D prime left parenthesis negative 8 comma 2 right parenthesis .
Rectangle A′B′C′D′
has vertices A′(1,2)
, B′(1,8)
, and C′(8,8)
.
To reflect a point on the x-axis, we change the sign of the y-coordinate. And to reflect a point on the y-axis, we change the sign of the x-coordinate.
For the rectangle ABCD (A(-1,-2), B(-1,-8), C(-8,-8), D(-8,-2)), the reflected points on the x-axis would be A'(-1,2), B'(-1,8), C'(-8,8), and D'(-8,2). This is because we change the sign of the y-coordinate for each point.
And the reflected points on the y-axis would be A'(1,-2), B'(1,-8), C'(8,-8), and D'(8,-2). This is because we change the sign of the x-coordinate for each point.
Therefore, the coordinates of the vertices for rectangle A'B'C'D' are A'(1,2), B'(1,8), C'(8,8), and D'(8,2).
Hence, the correct answer is Rectangle A′B′C′D′ has vertices A′(1,2), B′(1,8), C′(8,8), and D′(8,2).
Rotate the point (9, 5)
on a line segment 180 degrees clockwise. What is the new point?(1 point)
Responses
(−5,−9)
left parenthesis negative 5 comma negative 9 right parenthesis
(−9, −5)
left parenthesis negative 9 comma negative 5 right parenthesis
(9, −5)
left parenthesis 9 comma negative 5 right parenthesis
(5, 9)
To rotate a point (x, y) 180 degrees clockwise on the coordinate plane, we need to change the signs of both the x and y coordinates.
For point (9, 5), the x-coordinate becomes -9 and the y-coordinate becomes -5.
Therefore, the new point after rotating 180 degrees clockwise is (-9, -5).
Hence, the correct answer is (−9, −5).