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2 years ago

What is the slope of a line perpendicular to the line that passes through (4, -3) and

Mathematics

1 answer:

m_a_m_a [10]2 years ago

4 0

Answer:

1/2

Step-by-step explanation:

The slope of the points (4,-3) and (3,-1) is -2

The slope of a line perpendicular to said points would be the opposite reciprocal which would be 1/2

heres how you'd find the initial slope of the points

(4, -3)

-1 +2

(3, -1)

Slope= rise/run= 2/-1= -2

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2 years ago

Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.

koban [17]

Answer:

$x^2 + 4x + y^2 +8y = 0$

Step-by-step explanation:

Given

$A = (-1,-2)$

$B = (2,4)$

$AP:BP = 1 : 2$

Required

The locus of P

$AP:BP = 1 : 2$

Express as fraction

$\frac{AP}{BP} = \frac{1}{2}$

Cross multiply

$2AP = BP$

Calculate AP and BP using the following distance formula:

$d = \sqrt{(x - x_1)^2 + (y - y_1)^2}$

So, we have:

$2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

$2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

Take square of both sides

$4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2$

Evaluate all squares

$4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16$

Collect and evaluate like terms

$4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20$

Open brackets

$4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20$

Collect like terms

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$3x^2 + 12x + 3y^2 +24y = 0$

Divide through by 3

$x^2 + 4x + y^2 +8y = 0$

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Naddik [55]

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3 years ago

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natta225 [31]

Answer:

Upper left: the answer is 2, becuase 2 times 5x = 10x

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Lower left: the answer is 3, because 3 times 3a+2b = 9a+6b

Lower right: the answer is 3a+2b, because 4 times 3a+2b =12b+8b

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2 years ago