Mathematics, 21.07.2020 17:01 jamisoncameron000

A(7-1), B(6, 4) and C(5, 5) are three points in a plane.
1). Find the equations of the
perpendicular bisectors of AB and AC
(ü) Determine the point of
intersection of the perpendicular
bisectors in (i).
(WAEC)

Answers: 1

Show answers

Answers

Answer from: hgcmj

The answer is below

Step-by-step explanation:

The equation of the line passing through two points is given by:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\$

The equation of line AB is:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-(-1)=\frac{4-(-1)}{6-7}(x-7)\\\\y+1=-5(x-7)\\y+1=-5x+35\\y=-5x+34$

The midpoint of two lines is given as:

$x=\frac{x_1+x_2}{2}, y=\frac{y_1+y_2}{2}\\midpoint\ of\ AB \ is:\\x=\frac{7+6}{2}=6.5, y=\frac{-1+4}{2}=1.5\\ = (6.5,1.5)$

The equation of line AC is:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-(-1)=\frac{5-(-1)}{5-7}(x-7)\\\\y+1=-3(x-7)\\y+1=-3x+21\\y=-3x+20$

The midpoint of two lines is given as:

$x=\frac{x_1+x_2}{2}, y=\frac{y_1+y_2}{2}\\midpoint\ of\ AB \ is:\\x=\frac{7+5}{2}=6, y=\frac{-1+5}{2}=2\\ = (6,2)$

The product of the slope of a perpendicular bisector of a line and the slope of the line is -1. That is m1m2 = -1

The slope of the perpendicular bisector of AB is:

m(-5)=-1

m=1/5

The equation of the perpendicular bisector of AB passing through (6.5,1.5) is:

$y-y_1=m(x-x_1)\\y-1.5=\frac{1}{5}(x-6.5)\\y=\frac{1}{5} x-8.25$

The slope of the perpendicular bisector of AB is:

m(-3)=-1

m=1/3

The equation of the perpendicular bisector of AB passing through (6,2) is:

$y-y_1=m(x-x_1)\\y-2=\frac{1}{3}(x-7)\\y=\frac{1}{3} x-4.33$

2) The point of intersection is gotten by solving y = 1/5 x -8.25 and y = 1/3 x-4.33 simultaneously.

Subtracting the two equations from each other gives:

0= -0.133x - 3.92

-0.133x = 3.92

x = -29.5

Put x = -29.5 in y = 1/5 x -8.25 i.e:

y = 1/5 (29.5) -8.25

y = -14.16

The point of intersection is (-29.5, -14.16)

Answer from: Quest

a. 19,958,400

step-by-step explanation:

hope this

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Another question on Mathematics

Mathematics, 21.06.2019 18:20

Do social recommendations increase ad effectiveness? a study of online video viewers compared viewers who arrived at an advertising video for a particular brand by following a social media recommendation link to viewers who arrived at the same video by web browsing. data were collected on whether the viewer could correctly recall the brand being advertised after seeing the video. the results are given below.correctly recalled the brandarrival 409153browsing20484b. conduct the hypothesis test, using the 0.025 level of significance.what is the value of the test statistic? χ2stat=what is the p-value? p-value=is this value significant atα=0.025?

Answers: 2

Answer

Mathematics, 21.06.2019 21:50

5. which description does not guarantee that a quadrilateral is a squar ajo is a parallelogram with perpendicular diagonals 0% has all sides congruent and all angles congruent o has all right angles and has all sides congruent 10% is both a rectangle and a rhombus 30%

Answers: 2

Answer

Mathematics, 21.06.2019 21:50

What is the next step in the given proof? choose the most logical approach. a. statement: m 1 + m 2 + 2(m 3) = 180° reason: angle addition b. statement: m 1 + m 3 = m 2 + m 3 reason: transitive property of equality c. statement: m 1 = m 2 reason: subtraction property of equality d. statement: m 1 + m 2 = m 2 + m 3 reason: substitution property of equality e. statement: 2(m 1) = m 2 + m 3 reason: substitution property of equality

Answers: 3

Answer

Mathematics, 22.06.2019 00:40

Calculate the effective quarterly compound interest rate equivalent to a 1% of monthly compound interest rate.

Answers: 3

Answer

You know the right answer?

A(7-1), B(6, 4) and C(5, 5) are three points in a plane.
1). Find the equations of the
pe...

Questions

Mathematics, 05.05.2020 12:30

Determine the zeros of y = 2.2 + 3x . Select all that apply.