Question

in the diagram the points A and C lie on the x and y axis respectively and the equation AC is 2y+x=16. The point B has coordinates (2,2). The perpendicular lone from B to AC is at the point X
(i) find the coordinates of X​

Answer 1

Answer:

The coordinates of X  is (4, 6).

Step-by-step explanation:

Step 1:

The equation of AC  is image.

Rewrite the equation in the slope -intercept  form : image.

image

Subtract x on each side.

image

Divide each side by 2.

image

Compare the above equation with standard form.

Slope image and y - intercept is 8.

Step 2:

The perpendicular from point B to AC meets AC at the point X.

The slope of the perpendicular to line AC is image.

Point slope form of equation is image.

Substitute slope image and point image.

image

A line perpendicular to AC is image.

Step 3:

Find the point of intersection of line  image and its perpendicular  image.

image

Substitute x = 4 in image.

image

The point of intersection line AC and the perpendicular from B to AC is X = (4, 6).