geometery cumilitive review 7

Question

question 1.what is an equation of a line which passes through (6,9) and is perpendicular to the line whose equation is 4x-6y=15?

question 2.In the diagram line AC has endpoints with coordinates A(-5,2) and C(4,-10) If B is a point on line AC and AB:AC=1:2 what are the coordinates of B?

question 3.In the graph triangle abc has coordinates a(-9,2) b(-6,-6) and c(-3,-2) and triangle rst has coordinates r(-2,9) s(5,6) and t(2,3) is triangle abc congruent to triangle rst? justify your answer

question 4. triangle DAN has verticles and coordinates D(-6,-1) A(6,3) and N(-3,10) find the area of triangle DAN

Answer 1

#1. m=2/3 for line ,,, perpendicular slope is -1/(2/3)=-(3/2)

line is -(3/2)=(y-9)/(x-6)

y=-(3/2)x+18

#2. x coordinate = (-5+4)/2

y coordinate = (2-10)/2

#3. ab²=8²+3²,,,,,bc²=4²+3²,,,,ca²=4²+6²

for triangles to be congruent, all side lengths of one must equal corresponding side lengths of other

rs²=3²+3²,,,,,,rs not equal to any side of abc, so rst not congruent

#4. area = (1/2)*base*altitude

take base as DA, DA=4√10 by distance formula

DA has equation y=(1/3)x+1

distance from point (x₀,y₀) to line y=mx+b is by similar triangle proof

d=|mx₀+b-y₀|/√(1+m²)

here d=|(1/3)(-3)+1-10|/√√(10/9)

d=3√10

area=60