1) find the coordinate of the image of point (1,2) translated left 2 units and reflected over the x -axis
2) Find the coordinate of the image of the point (2, -4) reflected over the x-axis
3) Determine the midpoint of the segment whose endpoints are A(7, 3, -4) and B(-3, 1, 0)
4) Find coordinates of the image of point (2,-1) translated up 3 units
5) Find the coordinates of the image of the point (5, -1) dilated with center at origin scale factor 3
6) Find the coordinates of the image of point (5,2) translatd down 4 units and left 1 unit..
Can someone please help me with these problems ?
I was trying to find a 10 answers but there is none here
1) To translate the point (1, 2) left 2 units, subtract 2 from the x-coordinate:
New x-coordinate = 1 - 2 = -1
To reflect the translated point over the x-axis, negate the y-coordinate:
New y-coordinate = -2
Therefore, the coordinate of the image of the point (1, 2) translated left 2 units and reflected over the x-axis is (-1, -2).
2) To reflect the point (2, -4) over the x-axis, negate the y-coordinate:
New y-coordinate = -(-4) = 4
Therefore, the coordinate of the image of the point (2, -4) reflected over the x-axis is (2, 4).
3) To find the midpoint of the segment with endpoints A(7, 3, -4) and B(-3, 1, 0), take the average of the x-coordinates, y-coordinates, and z-coordinates:
Midpoint x-coordinate = (7 + (-3)) / 2 = 4 / 2 = 2
Midpoint y-coordinate = (3 + 1) / 2 = 4 / 2 = 2
Midpoint z-coordinate = (-4 + 0) / 2 = -4 / 2 = -2
Therefore, the midpoint of the segment AB is (2, 2, -2).
4) To translate the point (2,-1) up 3 units, add 3 to the y-coordinate:
New y-coordinate = -1 + 3 = 2
Therefore, the coordinates of the image of the point (2,-1) translated up 3 units is (2, 2).
5) To dilate the point (5, -1) with a center at the origin and a scale factor of 3, multiply both the x-coordinate and y-coordinate by the scale factor:
New x-coordinate = 5 * 3 = 15
New y-coordinate = -1 * 3 = -3
Therefore, the coordinates of the image of the point (5, -1) dilated with a center at the origin and a scale factor of 3 is (15, -3).
6) To translate the point (5, 2) down 4 units, subtract 4 from the y-coordinate:
New y-coordinate = 2 - 4 = -2
To translate the point left 1 unit, subtract 1 from the x-coordinate:
New x-coordinate = 5 - 1 = 4
Therefore, the coordinates of the image of the point (5, 2) translated down 4 units and left 1 unit is (4, -2).
Sure! I can help you with these problems. Let's go through each question step by step.
1) To find the image of point (1,2) translated left 2 units and reflected over the x-axis, you first need to translate the point left by 2 units. This means subtracting 2 from the x-coordinate of the point. So the translated point becomes (-1,2). Next, to reflect it over the x-axis, you need to change the sign of the y-coordinate. Therefore, the image of the point (1,2) after translation and reflection is (-1,-2).
2) To find the image of the point (2,-4) reflected over the x-axis, you just need to change the sign of the y-coordinate. Therefore, the image of the point (2,-4) after reflection is (2,4).
3) To find the midpoint of the segment whose endpoints are A(7, 3, -4) and B(-3, 1, 0), you need to find the average of the x-coordinates, the average of the y-coordinates, and the average of the z-coordinates.
The x-coordinate of the midpoint is (7 + (-3))/2 = 4/2 = 2.
The y-coordinate of the midpoint is (3 + 1)/2 = 4/2 = 2.
The z-coordinate of the midpoint is (-4 + 0)/2 = -4/2 = -2.
Therefore, the midpoint of the segment AB is (2, 2, -2).
4) To find the image of the point (2,-1) translated up 3 units, you need to add 3 to the y-coordinate of the point. So the translated point becomes (2,2).
5) To find the image of the point (5,-1) dilated with a center at the origin and a scale factor of 3, you need to multiply both the x-coordinate and the y-coordinate by the scale factor.
The x-coordinate becomes 5 * 3 = 15.
The y-coordinate becomes -1 * 3 = -3.
Therefore, the image of the point (5,-1) after dilation is (15, -3).
6) To find the image of the point (5,2) translated down 4 units and left 1 unit, you need to subtract 4 from the y-coordinate and subtract 1 from the x-coordinate.
The x-coordinate becomes 5 - 1 = 4.
The y-coordinate becomes 2 - 4 = -2.
Therefore, the image of the point (5,2) after translation is (4, -2).
I hope this helps! Let me know if you have any further questions.
Why not just take a piece of graph paper and perform the stated operations ?
In each case your answer will be intuitively obvious