Functions(2)







The Distance Formula is derived from the Pythagorean Theorem. To find the distance between two points all that you need to do is use the coordinates of the ordered pairs and apply the distance formula.  media type="custom" key="3943873"
 * = Given the points (-4,2) and (5,7), apply the Distance Formula ||= Steps to Solve ||
 * = [[image:distance_formula_for_table.png width="302" height="47"]] ||= Distance Formula ||
 * = [[image:distance_formula_step_2.png]] ||= Substitute in all the points ||
 * = [[image:distance_formula_step_3.png]] ||= Simplify ||
 * = [[image:distance_formula_step_4.png]] ||= Simplify ||
 * = [[image:distance_formula_step_5.png]] ||= Use a calculator ||

The Midpoint formula is used when you need to find the point that is exactly between two other points. The midpoint formula is applied when you need to find a line that bisects a certain line segment. The 'middle point' is called the "midpoint".

<span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;"> media type="custom" key="3943855" [|Click Here For An Interactive Midpoint Website] <span style="font-family: 'Arial','sans-serif';">Most of the time it is easy to determine the solution points that have zero as either an x-coordinate or y-coordinate. These points are called intercepts because they are the points where the graph touches or intersects the x or y axis. Graphs can have no intercepts, one intercept or several intercepts. ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Plug in 0 for y ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Has the solution x=-2, x-int=(-2,0) || ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Plug in 0 for x ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Has the solution y=4, y-int=(0,4) || <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">
 * <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Given the points (6,-3) and (8,5), find the midpoint. || <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Steps to Solve ||
 * <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">[[image:midpoint_formula_step_1.png]] || <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Midpoint Formula ||
 * <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">[[image:midpoint_formula_step_2.png]] || <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Substitute in all the points ||
 * <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">[[image:midpoint_formula_step_3.png]] || <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Simplify ||
 * ~ <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Find the x and y intercepts of the graph of y=2x+4 ||
 * = <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Solutions ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Steps ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Answers ||
 * = <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">0 =2x+4=
 * = <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">y =2(0)+4=

This basic technique is used for sketching the graph of an equation is called the point plotting technique. [|Here For An Interactive Intercept Website]

When you know the symmetry of a graph before you attempt to sketch it very helpful. This is because then you only need half as many solution points to sketch the graph (there are three basic types of symmetry).

<span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Symmetry of Origin
 * ~ <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Rules (Check For Symmetry Algerbraically) ||~ <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;"> ||~ <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;"> ||~ <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;"> ||
 * = <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Symmetric with respect to Origin ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">(x,y) ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">---> ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">(-x,-y) ||
 * = <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Symmetric with respect to y-axis ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">(x,y) ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">---> ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">(-x,y) ||
 * = <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Symmetric with respect to x-axis ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">(x,y) ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">---> ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">(x,-y) ||
 * = <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Symmetric with respect to y=x ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">(x,y) ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">---> ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">(y,x) ||
 * = <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Symmetric with respect to y=-x ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">(x,y) ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">---> ||= <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">(-y,-x) ||
 * = <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Equations symmetric with respect to the y-axis are known as EVEN ||
 * = <span style="display: block; font-family: 'Arial Black',Gadget,sans-serif; text-align: center;">Equations symmetric with respect to the origin are known as ODD ||

Symmetry of X-axis Symmetry of Y-axis



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