contestada


CD is perpendicular to AB and passes through point C5, 12).
If the coordinates of A and Bare (-10,-3) and (7, 14), respectively, the x-intercept of CD is
The point
lies on CD.

Respuesta :

Cricetus

Answer:

x intercept of CD = 17

Step-by-step explanation:

We are given a line AB with its end coordinates. and Another line segment CD which is perpendicular to AB. We have the coordinates of C , and we are asked to find the x intercept of line CD.

For that we need to find the equation of CD

we have coordinates of C , and hence if we have slope of CD we can find equation of CD

Slope of CD can be determine with the help of slope of AB as CD⊥ AB

So, the slope of CD [tex]mCD = -\frac{1}{mAB}[/tex]

Hence we start from determining slope of AB

slope is given as

[tex]m= \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m= \frac{14-(-3)}{7-(-10)}=\frac{17}{17}=1[/tex]

Hence [tex]mAB=1[/tex]

There fore [tex]mCD=-1[/tex]

(∵  Product of Slopes of two perpendicular lines is always -1)

Now we find the equation of CD with the help of slope -1 and coordinates of C(5,12)

[tex]m=\frac{y-y_1}{x-x_1}[/tex]

[tex]-1=\frac{y-12}{x-5}[/tex]

[tex]-x+5=y-12[/tex]

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

Hence we have our equation , now in order to find the x intercept we keep y = 0 in it and solve for x

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

[tex]x=17[/tex]

Hence the x intercept is 17

Ver imagen Cricetus
raphealnwobi

The x-intercept of CD line with equation y = x + 7 is point (0, -7)

What is a linear equation?

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the initial value of y.

Two lines are perpendicular if the product of their slopes is -1.

Given that the coordinates of A and Bare (-10,-3) and (7, 14), hence:

Slope of AB = (14 - (-3)) / (7 - (-10)) = 1

Since CD is perpendicular to AB, the slope of CD is 1.

CD passes through point C(5, 12), The equation of line CD is:

y - 12 = 1(x - 5)

y = x + 7

The x intercept of CD is at y = 0:

0 = x + 7

x = -7

The x-intercept of CD line with equation y = x + 7 is point (0, -7)

Find out more on linear equation at: https://brainly.com/question/14323743

Otras preguntas