The answer would be a) 14 sqrt 6
<h3>1.</h3>
The equation in point-slope form: y - y₁ = m(x - x₁)
slope: m = -2
point: (4, -5) ⇒ x₁ = 4, y₁ = -5
Therefore, the equation of the line in point-slope form:
<h3>
y + 5 = -2(x - 4)</h3>
<h3>2.</h3>
The equation in slope-intercept form: y = mx + b
Parallel lines has the same slope, so:
y = 4x + 2 ⇒ a = 4
If a line passes through the point <em>(x₁, y₁) </em>then the equation y<em>₁</em> = mx<em>₁</em> + b is true.
(4, 6) ⇒ x₁ = 4, y₁ = 6
So: 6 = 4·4 + b ⇒ b = -10
Therefore the equation:
<h3>
y = 4x - 10</h3>
<h3>3.</h3>
a = 3
(-1, 1) ⇒ x₁ = -1, y₁ = 1
So: 1 = 3·(-1) + b ⇒ b = 4
The equation:
<h3>
y = 3x + 4</h3>
<h3>4. </h3>
The product of slopes of perpendicular lines is -1.
2x - 7y = 1 ⇒ 7y = -2x + 1 ⇒ y = -²/₇x + ¹/₇
-²/₇×m = -1 ⇒ m = ⁷/₂
(0, -4) ⇒ x₁ = 0, y₁ = -4
-4 = ⁷/₂·0 + b ⇒ b = -4
The equation:
<h3>
y = ⁷/₂x - 4</h3>
Do you know what a transformation is
The intersecting secants theorem says
That is, for either secant line, you take the length of the part of the secant line outside the circle (6 and 5 in this case) and multiply it by the "total" length of the secant line between the point where the two secant lines intersect and the furthest point where the secant touches the circle (6+12=18 and 5+x in this case). The theorem says these products are equal.
Then
