Geometry

Use the figure to the right to find the value of PT. T is the midpoint of PQ [Segment] PT=3x+5 and TQ=5x−7

(1) Subtract 3x from both sides [5=2x-7] (2) Add 7 to both sides [12=2x] (3) Divide 12 by 2 [X=6] (4) Solve Pt by adding 6.

Write the equation in​ slope-intercept form. 5x+4y=24

(1) Subtract 5x from both sides. {4y=24-5x} (2) Divide both sides by 24 by 4 and 5 by 4 (3) y= -5/4x+6

Find the midpoint of the line segment joining the points ​R( −5​,5​) and ​S(2​,7​).

Formula for midpoint is: X1+X2 divide by 2, Y1+y2/2 (1)Add -5 plus 2 = -3 divided by 2 Is -3/2 [X equals -3/2] (2) Add 5 to 7= 12 divided by 2 and get 6 (Y equals 6)

Find the slope of the line containing the pair of points. ​(−5​,−2​) and ​(−1​,−7​)

Formula: [Y2-Y1 over X2-X1] (1) -7-(-2)=-5 (2) -1-(-5)=4 (3) [Answer -5/4]

Use the number line​ below, where RS=5y+5​, ST=2y+3​, and RT=11y−16. a. What is the value of​ y? b. Find​ RS, ST, and RT.

(1) 5y+5+ 2y+3 = 11-16 (Combine like terms) (2)7y+8=11y-16 (Add 16 to 8) (3) 7y+24=11y (Subtract 7y from 11y) (4)24=4y (Divide 4 by 24) [Answer is 6]

Write an equation for the line parallel to the given line that contains C. C( 4 , 8 ) y= -3x+5

(1) Find the slope which is -3 [Same slope if parallel] Point-slope form: Y-Y1=m(x-x1) y-8= -3(x-4) -8=-3x-12 (Add 8 to -12=20) Y=-3x+20

Find the distance between the points. ​(0​,7​) and ​(−3​,7​)

Formula: (X2-X1)2+(Y2-y1)2 (1) -3-0= -3(Square)=9 (2) 7-7=0(Square)=0 (3) Add 9 + 0=9 (4) Square 9 =3

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.) midpoint ​(- 17​,- 16​), endpoint ​(- 8,−7​)

Formula: X1+x2/2, y1+y2/2 (1) -8+x2/2= -17 (Substitute -8 for X1 ) (2) Multiple 2 X -17= -34, Subtract -8 from -34 (3) Repeat the steps for Y.

Write an equation of the line perpendicular to the given line that contains P. ​P(3,−4​); y 1y=1/6x+1

Slope is -6 y-(-4)= -6(x-3) Answer: y+4=-6(x-3)