Find the points that are symmetric to given point (a) across the x axis, (b) across the y axis, and (c) across the origin
1. (1,4)
2. (2,-3)
3. Find equations for the vertical and horizontal lines through the point (1,3)
8. Given the point, P(6,0) and the line, L:2x-y=-2
A. Find an equation for the line through P parallel to L
B. Find an equation of the line through P perpendicular to L
Hi yitsongg,
1. Graph this point and let the x and y axes be the lines of symmetry.
(1, 4) reflected across the x axis is (1, -4) and reflected across the y-axis is (-1, 4). With respect to the origin, it would be (-1, -4).
2. See if you can handle this one based on the previous one.
3. The equation of the vertical line through (1, 3) is x = 1.
The equlation of the horizontal line through (1, 3) is y =3.
8. Recall that parallel lines have the same slope. Given line:
The slope is 2.
To find the equation of a line through (6, 0) with slope 2, use the slope intercept form of the equation and find the y-intercept.
Therefore, the equation of a line through (6, 0) and parallel to the line whose equation is 2x - y = -2 is y = 2x -12.
To find the equation of a line through (6, 0) and perpendicular to 2x - y = -2, use the negative reciprocal of the slope of this line (which is -1/2) and perform the same steps as above to find the y-intercept and ultimately, the equation in slope-intercept form.
and so on.