A complex point of the form a + 3i has a distance of 29 units from –9 + 24i. What is the value of a?

a = 11 or a = -29

Step-by-step explanation:

A: a+3i        B: -9+24i      AB = 29

AB² = (a - -9)² + (3 - 24)² = (a + 9)² + (-21)²

AB² = a² + 18a + 81 + 441 = 29² = 841

a² + 18a -319 = 0

a = (-18 ± √18²-4*1*(-319)) / 2 = (-18 ± √1600) / 2 = (-18 ± 40)/2

a = 11 or a = -29

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.