contestada

PLEASE
CD is perpendicular to AB and passes through point C(5, 12). If the coordinates of A and B are (-10, -3) and (7, 14), respectively, the x-intercept of CD is ____ . The point ____ lies on CD .


blank one
1)12,0
2)15,0
3)17,0
4)19,0


blank two

1)-5,24
2)-2,19
3)7,-10
4)8,11

Respuesta :

10simbahunde

First find the gradient of line AB

14--3/7--10

17/17 = 1

As CD is perpendicular to AB take the negative reciprocal of the gradient to AB to find gradient of CD

Gradient of CD = -1

to find y intercept use points given

12=(-1 x 5) +c

17 = c

C is the y intercept so for question 1 the answer is 3


for the second question just plug values into the equation and see if you get the right y value

Here the only number that works is -2

for question 2

the answer is 2



isyllus

Answer:

First blank (17,0)

Option 3 is correct

Second Blank (-2,19)

Option 2 is correct  

Step-by-step explanation:

CD is perpendicular to AB

C(5,12)

A(-10,-3)

B(7,14)

CD ⊥ AB

Thus, Slope of CD is negative inverse of slope of AB

[tex]\text{Slope of AB }=\dfrac{14+3}{7+10}[/tex]

                          [tex]m=1[/tex]

Slope of CD, m=-1  (CD ⊥ AB )

Point C: (5,12)

Equation of line CD,

[tex]y-12=-1(x-5)[/tex]

[tex]y=-x+17[/tex]

For x-intercept: Put y=0

[tex]0=-x+17[/tex]

[tex]x=17[/tex]

x-intercept: (17,0)

For second blank we have to check each point.

Option 1: (-5,24) ,Put x=-5 and y=24

[tex]24=5+17[/tex]

[tex]24\neq 22[/tex]

False

Option 2: (-2,19) ,Put x=-2 and y=19

[tex]19=2+17[/tex]

[tex]19=19[/tex]

True

Option 3: (7,-10) ,Put x=7 and y=-10

[tex]-10=-7+17[/tex]

[tex]-10\neq 10[/tex]

False

Option 4: (8,11) ,Put x=8 and y=11

[tex]11=-8+17[/tex]

[tex]11\neq 9[/tex]

False

Hence, First blank (17,0) and Second blank (-2,19)