The most used formula about this is the distance formula. If you want to find the distance between (x1,y1) and (x2,y2), you may use the distance formula
distance=(x1−x2)2+(y1−y2)2=(△x)2+(△y)2.
Ron the Mouse travels 80 centimeters north and then 150 centimeters east.
Let d be the distance traveled by Ron the Mouse and s be the magnitude of the displacement of the mouse.
Find the value (in centimeters) of d−s.
The midpoint formula might come in handy, too. The midpoint of (x1,y1) and (x2,y2) is
(2x1+x2,2y1+y2).
Let O=(0,0),P=(3,4),Q=(6,0) be the vertices of triangle OPQ. Point R inside the triangle is such that triangles OPR,PQR,OQR are of equal area.
The product of the coordinates of R is __________.
Equation of Lines
The equation of lines is in the form of y=mx+n (where m is the slope and n is the y-intercept), or ax+by=c.
What is the equation of the line passing through (3,7) and (5,4)?
Put the coordinates into y=mx+n and get 7=3m+n and 5=4m+n.
Solve it and get m=−1.5 and n=11.5, so the equation is y=−1.5x+11.5 or 3x+2y=23.□
The lines x=4y−a and y=4x−b intersect at the point (1,2). What is a+b?
Equation of Other Curves
The equation of conic sections are in the form of Ax2+Bxy+Cy2+Dx+Ey+F=0.
In the ellipse shown, let a and b be the lengths of the semi-major and semi-minor axes, respectively.