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How do you find linear equations with just coordinates?
if we take the (x1,y1),(x2,y2) as coordinates the formula was (x-x1)/(x2-x1)=(y-y1)/(y2-y1)
M is the midpoint of pq verify that this is the midpoint by using the distance formula to show tha pm equals mq?
Let P(x1, y1), Q(x2, y2), and M(x3, y3).If M is the midpoint of PQ, then,(x3, y3) = [(x1 + x2)/2, (y1 + y2)/2]We need to verify that,√[[(x1 + x2)/2 - x1]^2 + [(y1 + y2)/2 - y1]^2] = √[[x2 - (x1 + x2)/2]^2 + [y2 - (y1 + y2)/2]^2]]Let's work separately in both sides. Left side:√[[(x1 + x2)/2 - x1]^2 + [(y1 + y2)/2 - y1]^2]= √[[(x1/2 + x2/2)]^2 - (2)(x1)[(x1/2 + x2/2)) + x1^2] + [(y1/2 + y2/2)]^2 - (2)(y1)[(y1/2 + y2/2)] + y1^2]]= √[[(x1)^2]/4 + [(x1)(x2)]/2 + [(x2)^2]/4 - (x1)^2 - (x1)(x2) + (x1)^2 +[(y1)^2]/4 + [(y1)(y2)]/2 + [(y2)^2]/4 - (y1)^2 - (y1)(y2) + (y1)^2]]= √[[(x1)^2]/4 - [(x1)(x2)]/2 + [(x2)^2]/4 + [(y1)^2]/4 - [(y1)(y2)]/2 + [(y2)^2]/4]]Right side:√[[x2 - (x1 + x2)/2]^2 + [y2 - (y1 + y2)/2]^2]]= √[[(x2)^2 - (2)(x2)[(x1/2 + x2/2)] + [(x1/2 + x2/2)]^2 + [(y2)^2 - (2)(y2)[(y1/2 + y2/2)] + [(y1/2 + y2/2)]^2]]= √[[(x2)^2 - (x1)(x2) - (x2)^2 + [(x1)^2]/4 + [(x1)(x2)]/2 + [(x2)^2]/4 + (y2)^2 - (y1)[(y2) - (y2)^2 + [(y1)^2]/4) + [(y1)(y2)]/2 + [(y2)^2]/4]]= √[[(x1)^2]/4 - [(x1)(x2)]/2 + [(x2)^2]/4 + [(y1)^2]/4 - [(y1)(y2)]/2 + [(y2)^2]/4]]Since the left and right sides are equals, the identity is true. Thus, the length of PM equals the length of MQ. As the result, M is the midpoint of PQ
What does slope mean in math class?
slope is the steepness of a line, it is defined by the change in the y values divided by the change in the x values of any two points on a line (x1, y1) and (x2, y2) slope = (y1 - y2)/(x1 - x2)
How to get the equation of a line that passes through these two points?
(y-y1)=(y2-y1/x2-x1)(x-x1)
How do you solve for slope from two points and a graph?
Points: (x1, y1) and (x2, y2) Slope: y1-y2/x1-x2
C program to design a car?
#include<stdio.h> #include<graphics.h> #include<math.h> #include<conio.h> #include<dos.h> #include<alloc.h> #include<stdlib.h> #define RAD 3.141592/180 class fig { private: int x1,x2,y1,y2,xinc,yinc; public: void car() { xinc=10;yinc=10; x1=y1=10; x2=x1+90;y2=y1+35; int poly[]={x1+5,y1+10,x1+15,y1+10,x1+20,y1,x1+50,y1,x1+60,y1+10,x1+90,y1+17,x1+90,y1+20,x1+5,y1+20,x1+5,y1+10}; setfillstyle(SOLID_FILL,LIGHTGRAY); setlinestyle(SOLID_LINE,1,2); setcolor(4); drawpoly(9,poly); line(x1+15,y1+10,x1+60,y1+10); line(x1+20,y1+10,x1+20,y1); line(x1+35,y1+10,x1+35,y1); line(x1+50,y1+10,x1+50,y1); floodfill(x1+18,y1+8,4); floodfill(x1+28,y1+8,4); floodfill(x1+36,y1+8,4); floodfill(x1+52,y1+8,4); setfillstyle(SOLID_FILL,4); floodfill(x1+18,y1+12,4); setfillstyle(SOLID_FILL,BLUE); bar(x1+5,y1+20,x1+90,y1+25); setcolor(DARKGRAY); circle(x1+20,y1+25,8); circle(x1+20,y1+25,6); setfillstyle(1,8); floodfill(x1+21,y1+25,8); circle(x1+70,y1+25,8); circle(x1+70,y1+25,6); floodfill(x1+71,y1+25,8); int size=imagesize(x1,y1,x2,y2); void far *buf=farmalloc(size); getimage(x1,y1,x2,y2,buf); while(!kbhit()) { putimage(x1,y1,buf,XOR_PUT); x1+=xinc;x2+=xinc; if(x2<(getmaxx()-10)) putimage(x1,y1,buf,COPY_PUT); else { cleardevice(); x1=10;x2=x1+90; y1+=yinc;y2+=yinc; if(y2<(getmaxy()-10)) { putimage(x1,y1,buf,COPY_PUT); } else {y1=10;y2=y1+35;} } delay(200); } farfree(buf); getch(); } } } } void main() { int gd=DETECT,gm; initgraph(&gd,&gm,"d:\\cplus"); fig f; f.car(); cleardevice(); closegraph(); }
How do you draw a square using line command?
Line (x1, y1, x2, y1); Line (x2, y1, x2, y2); Line (x2, y2, x1, y2); Line (x1, y2, x1, y1);
When using the slope formula does it have to be (y2-y1)(x2-x1) or can it be (y1-y2)(x1-x2)?
Oh, don't you worry, friend! When using the slope formula, whether you do (y2-y1)/(x2-x1) or (y1-y2)/(x1-x2), the answer will be the same! It's all about the difference in vertical and horizontal values, and as long as you stay consistent in your calculations, you'll find the slope just fine. Just trust your instincts and enjoy the process of solving the equation.
How do you find linear equations with just coordinates?
if we take the (x1,y1),(x2,y2) as coordinates the formula was (x-x1)/(x2-x1)=(y-y1)/(y2-y1)
What is the midpoint in math terms?
GIven 2 distance points (x1,y1) and (x2,y2) we can draw a line between those point and the midpoint formula finds the midpoint of that line. Call the midpoint (m1,m2) then it is [ (x1+x1 )/2 , (y1+y2/2)]
How do you find the equation of a line when given 2 coordinates?
(y -y1)=(x -x1)(y2 -y1)/(x2 -x1) defines the line containing coordinates (x1,y1) and (x2.y2).
What does the point slope formula look like?
y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) is a point on the line.
M is the midpoint of pq verify that this is the midpoint by using the distance formula to show tha pm equals mq?
Let P(x1, y1), Q(x2, y2), and M(x3, y3).If M is the midpoint of PQ, then,(x3, y3) = [(x1 + x2)/2, (y1 + y2)/2]We need to verify that,√[[(x1 + x2)/2 - x1]^2 + [(y1 + y2)/2 - y1]^2] = √[[x2 - (x1 + x2)/2]^2 + [y2 - (y1 + y2)/2]^2]]Let's work separately in both sides. Left side:√[[(x1 + x2)/2 - x1]^2 + [(y1 + y2)/2 - y1]^2]= √[[(x1/2 + x2/2)]^2 - (2)(x1)[(x1/2 + x2/2)) + x1^2] + [(y1/2 + y2/2)]^2 - (2)(y1)[(y1/2 + y2/2)] + y1^2]]= √[[(x1)^2]/4 + [(x1)(x2)]/2 + [(x2)^2]/4 - (x1)^2 - (x1)(x2) + (x1)^2 +[(y1)^2]/4 + [(y1)(y2)]/2 + [(y2)^2]/4 - (y1)^2 - (y1)(y2) + (y1)^2]]= √[[(x1)^2]/4 - [(x1)(x2)]/2 + [(x2)^2]/4 + [(y1)^2]/4 - [(y1)(y2)]/2 + [(y2)^2]/4]]Right side:√[[x2 - (x1 + x2)/2]^2 + [y2 - (y1 + y2)/2]^2]]= √[[(x2)^2 - (2)(x2)[(x1/2 + x2/2)] + [(x1/2 + x2/2)]^2 + [(y2)^2 - (2)(y2)[(y1/2 + y2/2)] + [(y1/2 + y2/2)]^2]]= √[[(x2)^2 - (x1)(x2) - (x2)^2 + [(x1)^2]/4 + [(x1)(x2)]/2 + [(x2)^2]/4 + (y2)^2 - (y1)[(y2) - (y2)^2 + [(y1)^2]/4) + [(y1)(y2)]/2 + [(y2)^2]/4]]= √[[(x1)^2]/4 - [(x1)(x2)]/2 + [(x2)^2]/4 + [(y1)^2]/4 - [(y1)(y2)]/2 + [(y2)^2]/4]]Since the left and right sides are equals, the identity is true. Thus, the length of PM equals the length of MQ. As the result, M is the midpoint of PQ
What does slope mean in math class?
slope is the steepness of a line, it is defined by the change in the y values divided by the change in the x values of any two points on a line (x1, y1) and (x2, y2) slope = (y1 - y2)/(x1 - x2)
What is the formula to calculate the slope?
It's m = y2 - y1/ x2- x1 It's m equals y2 minus y1 over x2 minus x1
How to get the equation of a line that passes through these two points?
(y-y1)=(y2-y1/x2-x1)(x-x1)
What is a point slope form equation?
(y-y1)=m(x-x1) OR we can write it y=m(x-x1)+y1
